KILLED proof of input_fSTR2DFPSu.trs # AProVE Commit ID: 5b976082cb74a395683ed8cc7acf94bd611ab29f fuhs 20230524 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 2 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 0 ms] (14) typed CpxTrs (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 2 ms] (16) TRS for Loop Detection (17) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (18) CpxWeightedTrs (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxTypedWeightedTrs (21) CompletionProof [UPPER BOUND(ID), 0 ms] (22) CpxTypedWeightedCompleteTrs (23) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) InliningProof [UPPER BOUND(ID), 730 ms] (28) CpxRNTS (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxRNTS (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (36) CdtProblem (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CpxRelTRS (43) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (44) CpxTRS (45) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CpxWeightedTrs (47) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CpxTypedWeightedTrs (49) CompletionProof [UPPER BOUND(ID), 0 ms] (50) CpxTypedWeightedCompleteTrs (51) NarrowingProof [BOTH BOUNDS(ID, ID), 536 ms] (52) CpxTypedWeightedCompleteTrs (53) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (54) CpxRNTS (55) InliningProof [UPPER BOUND(ID), 1217 ms] (56) CpxRNTS (57) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CpxRNTS (59) CompletionProof [UPPER BOUND(ID), 0 ms] (60) CpxTypedWeightedCompleteTrs (61) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (62) CpxRNTS (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms] (64) CdtProblem (65) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (74) CdtProblem (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (86) CdtProblem (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms] (92) CdtProblem (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 8 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 81 ms] (104) CdtProblem (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 14 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 123 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 21 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 89 ms] (116) CdtProblem (117) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 19 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (122) CdtProblem (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (128) CdtProblem (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 43 ms] (134) CdtProblem (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (140) CdtProblem (141) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 18 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 231 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 182 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 91 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 20 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 51 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 267 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 59 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 101 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 33 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 204 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 152 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 33 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 108 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 37 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 292 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 277 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 74 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 473 ms] (202) CdtProblem (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 53 ms] (204) CdtProblem (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 304 ms] (206) CdtProblem (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 62 ms] (208) CdtProblem (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 498 ms] (210) CdtProblem (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 67 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 145 ms] (214) CdtProblem (215) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 55 ms] (216) CdtProblem (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 207 ms] (218) CdtProblem (219) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 78 ms] (220) CdtProblem (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 190 ms] (222) CdtProblem (223) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 122 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 398 ms] (226) CdtProblem (227) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 94 ms] (228) CdtProblem (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 87 ms] (230) CdtProblem (231) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 443 ms] (232) CdtProblem (233) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 51 ms] (234) CdtProblem (235) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 131 ms] (236) CdtProblem (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 724 ms] (238) CdtProblem (239) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 105 ms] (240) CdtProblem (241) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 130 ms] (242) CdtProblem (243) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 456 ms] (244) CdtProblem (245) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 133 ms] (246) CdtProblem (247) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 75 ms] (248) CdtProblem (249) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 694 ms] (250) CdtProblem (251) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 137 ms] (252) CdtProblem (253) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 167 ms] (254) 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__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) a__sqr(0) -> 0 a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) a__dbl(0) -> 0 a__dbl(s(X)) -> s(s(dbl(X))) a__add(0, X) -> mark(X) a__add(s(X), Y) -> s(add(X, Y)) a__first(0, X) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) mark(terms(X)) -> a__terms(mark(X)) mark(sqr(X)) -> a__sqr(mark(X)) mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) mark(dbl(X)) -> a__dbl(mark(X)) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(recip(X)) -> recip(mark(X)) mark(s(X)) -> s(X) mark(0) -> 0 mark(nil) -> nil a__terms(X) -> terms(X) a__sqr(X) -> sqr(X) a__add(X1, X2) -> add(X1, X2) a__dbl(X) -> dbl(X) a__first(X1, X2) -> first(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__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) a__sqr(0') -> 0' a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) a__dbl(0') -> 0' a__dbl(s(X)) -> s(s(dbl(X))) a__add(0', X) -> mark(X) a__add(s(X), Y) -> s(add(X, Y)) a__first(0', X) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) mark(terms(X)) -> a__terms(mark(X)) mark(sqr(X)) -> a__sqr(mark(X)) mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) mark(dbl(X)) -> a__dbl(mark(X)) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(recip(X)) -> recip(mark(X)) mark(s(X)) -> s(X) mark(0') -> 0' mark(nil) -> nil a__terms(X) -> terms(X) a__sqr(X) -> sqr(X) a__add(X1, X2) -> add(X1, X2) a__dbl(X) -> dbl(X) a__first(X1, X2) -> first(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__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) a__sqr(0) -> 0 a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) a__dbl(0) -> 0 a__dbl(s(X)) -> s(s(dbl(X))) a__add(0, X) -> mark(X) a__add(s(X), Y) -> s(add(X, Y)) a__first(0, X) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) mark(terms(X)) -> a__terms(mark(X)) mark(sqr(X)) -> a__sqr(mark(X)) mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) mark(dbl(X)) -> a__dbl(mark(X)) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(recip(X)) -> recip(mark(X)) mark(s(X)) -> s(X) mark(0) -> 0 mark(nil) -> nil a__terms(X) -> terms(X) a__sqr(X) -> sqr(X) a__add(X1, X2) -> add(X1, X2) a__dbl(X) -> dbl(X) a__first(X1, X2) -> first(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0) -> c2 A__SQR(s(z0)) -> c3 A__SQR(z0) -> c4 A__DBL(0) -> c5 A__DBL(s(z0)) -> c6 A__DBL(z0) -> c7 A__ADD(0, z0) -> c8(MARK(z0)) A__ADD(s(z0), z1) -> c9 A__ADD(z0, z1) -> c10 A__FIRST(0, z0) -> c11 A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) A__FIRST(z0, z1) -> c13 MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) MARK(s(z0)) -> c23 MARK(0) -> c24 MARK(nil) -> c25 S tuples: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0) -> c2 A__SQR(s(z0)) -> c3 A__SQR(z0) -> c4 A__DBL(0) -> c5 A__DBL(s(z0)) -> c6 A__DBL(z0) -> c7 A__ADD(0, z0) -> c8(MARK(z0)) A__ADD(s(z0), z1) -> c9 A__ADD(z0, z1) -> c10 A__FIRST(0, z0) -> c11 A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) A__FIRST(z0, z1) -> c13 MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) MARK(s(z0)) -> c23 MARK(0) -> c24 MARK(nil) -> c25 K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__TERMS_1, A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, MARK_1 Compound Symbols: c_2, c1, c2, c3, c4, c5, c6, c7, c8_1, c9, c10, c11, c12_1, c13, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c20_2, c21_1, c22_1, c23, c24, c25 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0) -> c2 A__SQR(s(z0)) -> c3 A__SQR(z0) -> c4 A__DBL(0) -> c5 A__DBL(s(z0)) -> c6 A__DBL(z0) -> c7 A__ADD(0, z0) -> c8(MARK(z0)) A__ADD(s(z0), z1) -> c9 A__ADD(z0, z1) -> c10 A__FIRST(0, z0) -> c11 A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) A__FIRST(z0, z1) -> c13 MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) MARK(s(z0)) -> c23 MARK(0) -> c24 MARK(nil) -> c25 The (relative) TRS S consists of the following rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3 A__SQR(z0) -> c4 A__DBL(0') -> c5 A__DBL(s(z0)) -> c6 A__DBL(z0) -> c7 A__ADD(0', z0) -> c8(MARK(z0)) A__ADD(s(z0), z1) -> c9 A__ADD(z0, z1) -> c10 A__FIRST(0', z0) -> c11 A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) A__FIRST(z0, z1) -> c13 MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) MARK(s(z0)) -> c23 MARK(0') -> c24 MARK(nil) -> c25 The (relative) TRS S consists of the following rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0') -> 0' a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0') -> 0' mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3 A__SQR(z0) -> c4 A__DBL(0') -> c5 A__DBL(s(z0)) -> c6 A__DBL(z0) -> c7 A__ADD(0', z0) -> c8(MARK(z0)) A__ADD(s(z0), z1) -> c9 A__ADD(z0, z1) -> c10 A__FIRST(0', z0) -> c11 A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) A__FIRST(z0, z1) -> c13 MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) MARK(s(z0)) -> c23 MARK(0') -> c24 MARK(nil) -> c25 a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0') -> 0' a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> c:c1 c :: c2:c3:c4 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c:c1 A__SQR :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> c2:c3:c4 mark :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil MARK :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 c1 :: c:c1 0' :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil c2 :: c2:c3:c4 s :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c3 :: c2:c3:c4 c4 :: c2:c3:c4 A__DBL :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> c5:c6:c7 c5 :: c5:c6:c7 c6 :: c5:c6:c7 c7 :: c5:c6:c7 A__ADD :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> c8:c9:c10 c8 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c8:c9:c10 c9 :: c8:c9:c10 c10 :: c8:c9:c10 A__FIRST :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> c11:c12:c13 c11 :: c11:c12:c13 cons :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c12 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c11:c12:c13 c13 :: c11:c12:c13 terms :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c14 :: c:c1 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 sqr :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c15 :: c2:c3:c4 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 add :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c16 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 c17 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 dbl :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c18 :: c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 first :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c19 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 c20 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 recip :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 c23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 c24 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 nil :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil c25 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 a__terms :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil a__sqr :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil a__dbl :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil a__add :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil a__first :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil hole_c:c11_26 :: c:c1 hole_0':s:cons:terms:sqr:add:dbl:first:recip:nil2_26 :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil hole_c2:c3:c43_26 :: c2:c3:c4 hole_c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c254_26 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 hole_c5:c6:c75_26 :: c5:c6:c7 hole_c8:c9:c106_26 :: c8:c9:c10 hole_c11:c12:c137_26 :: c11:c12:c13 gen_0':s:cons:terms:sqr:add:dbl:first:recip:nil8_26 :: Nat -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c259_26 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__TERMS, mark, MARK, a__terms They will be analysed ascendingly in the following order: mark < A__TERMS A__TERMS = MARK mark < MARK mark = a__terms ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0') -> c2 A__SQR(s(z0)) -> c3 A__SQR(z0) -> c4 A__DBL(0') -> c5 A__DBL(s(z0)) -> c6 A__DBL(z0) -> c7 A__ADD(0', z0) -> c8(MARK(z0)) A__ADD(s(z0), z1) -> c9 A__ADD(z0, z1) -> c10 A__FIRST(0', z0) -> c11 A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) A__FIRST(z0, z1) -> c13 MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) MARK(s(z0)) -> c23 MARK(0') -> c24 MARK(nil) -> c25 a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0') -> 0' a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0') -> 0' a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0', z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0', z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0') -> 0' mark(nil) -> nil Types: A__TERMS :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> c:c1 c :: c2:c3:c4 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c:c1 A__SQR :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> c2:c3:c4 mark :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil MARK :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 c1 :: c:c1 0' :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil c2 :: c2:c3:c4 s :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c3 :: c2:c3:c4 c4 :: c2:c3:c4 A__DBL :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> c5:c6:c7 c5 :: c5:c6:c7 c6 :: c5:c6:c7 c7 :: c5:c6:c7 A__ADD :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> c8:c9:c10 c8 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c8:c9:c10 c9 :: c8:c9:c10 c10 :: c8:c9:c10 A__FIRST :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> c11:c12:c13 c11 :: c11:c12:c13 cons :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c12 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c11:c12:c13 c13 :: c11:c12:c13 terms :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c14 :: c:c1 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 sqr :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c15 :: c2:c3:c4 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 add :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c16 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 c17 :: c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 dbl :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c18 :: c5:c6:c7 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 first :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c19 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 c20 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 recip :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 c23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 c24 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 nil :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil c25 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 a__terms :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil a__sqr :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil a__dbl :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil a__add :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil a__first :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil hole_c:c11_26 :: c:c1 hole_0':s:cons:terms:sqr:add:dbl:first:recip:nil2_26 :: 0':s:cons:terms:sqr:add:dbl:first:recip:nil hole_c2:c3:c43_26 :: c2:c3:c4 hole_c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c254_26 :: c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 hole_c5:c6:c75_26 :: c5:c6:c7 hole_c8:c9:c106_26 :: c8:c9:c10 hole_c11:c12:c137_26 :: c11:c12:c13 gen_0':s:cons:terms:sqr:add:dbl:first:recip:nil8_26 :: Nat -> 0':s:cons:terms:sqr:add:dbl:first:recip:nil gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c259_26 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25 Generator Equations: gen_0':s:cons:terms:sqr:add:dbl:first:recip:nil8_26(0) <=> 0' gen_0':s:cons:terms:sqr:add:dbl:first:recip:nil8_26(+(x, 1)) <=> s(gen_0':s:cons:terms:sqr:add:dbl:first:recip:nil8_26(x)) gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c259_26(0) <=> c23 gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c259_26(+(x, 1)) <=> c14(c(c2, c23), gen_c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c259_26(x)) The following defined symbols remain to be analysed: a__terms, A__TERMS, mark, MARK They will be analysed ascendingly in the following order: mark < A__TERMS A__TERMS = MARK mark < MARK mark = a__terms ---------------------------------------- (15) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (16) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0) -> c2 A__SQR(s(z0)) -> c3 A__SQR(z0) -> c4 A__DBL(0) -> c5 A__DBL(s(z0)) -> c6 A__DBL(z0) -> c7 A__ADD(0, z0) -> c8(MARK(z0)) A__ADD(s(z0), z1) -> c9 A__ADD(z0, z1) -> c10 A__FIRST(0, z0) -> c11 A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) A__FIRST(z0, z1) -> c13 MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) MARK(s(z0)) -> c23 MARK(0) -> c24 MARK(nil) -> c25 The (relative) TRS S consists of the following rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (17) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (18) 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__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) [1] a__sqr(0) -> 0 [1] a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) [1] a__dbl(0) -> 0 [1] a__dbl(s(X)) -> s(s(dbl(X))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(add(X, Y)) [1] a__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] mark(terms(X)) -> a__terms(mark(X)) [1] mark(sqr(X)) -> a__sqr(mark(X)) [1] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(dbl(X)) -> a__dbl(mark(X)) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(X) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] a__terms(X) -> terms(X) [1] a__sqr(X) -> sqr(X) [1] a__add(X1, X2) -> add(X1, X2) [1] a__dbl(X) -> dbl(X) [1] a__first(X1, X2) -> first(X1, X2) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (19) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (20) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) [1] a__sqr(0) -> 0 [1] a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) [1] a__dbl(0) -> 0 [1] a__dbl(s(X)) -> s(s(dbl(X))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(add(X, Y)) [1] a__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] mark(terms(X)) -> a__terms(mark(X)) [1] mark(sqr(X)) -> a__sqr(mark(X)) [1] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(dbl(X)) -> a__dbl(mark(X)) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(X) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] a__terms(X) -> terms(X) [1] a__sqr(X) -> sqr(X) [1] a__add(X1, X2) -> add(X1, X2) [1] a__dbl(X) -> dbl(X) [1] a__first(X1, X2) -> first(X1, X2) [1] The TRS has the following type information: a__terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first cons :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first recip :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first mark :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first s :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first 0 :: recip:s:terms:cons:0:sqr:dbl:add:nil:first add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first nil :: recip:s:terms:cons:0:sqr:dbl:add:nil:first first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first Rewrite Strategy: INNERMOST ---------------------------------------- (21) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: mark_1 a__sqr_1 a__add_2 a__terms_1 a__dbl_1 a__first_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (22) 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__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) [1] a__sqr(0) -> 0 [1] a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) [1] a__dbl(0) -> 0 [1] a__dbl(s(X)) -> s(s(dbl(X))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(add(X, Y)) [1] a__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] mark(terms(X)) -> a__terms(mark(X)) [1] mark(sqr(X)) -> a__sqr(mark(X)) [1] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(dbl(X)) -> a__dbl(mark(X)) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(X) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] a__terms(X) -> terms(X) [1] a__sqr(X) -> sqr(X) [1] a__add(X1, X2) -> add(X1, X2) [1] a__dbl(X) -> dbl(X) [1] a__first(X1, X2) -> first(X1, X2) [1] The TRS has the following type information: a__terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first cons :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first recip :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first mark :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first s :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first 0 :: recip:s:terms:cons:0:sqr:dbl:add:nil:first add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first nil :: recip:s:terms:cons:0:sqr:dbl:add:nil:first first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first Rewrite Strategy: INNERMOST ---------------------------------------- (23) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (24) 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__terms(terms(X')) -> cons(recip(a__sqr(a__terms(mark(X')))), terms(s(terms(X')))) [2] a__terms(sqr(X'')) -> cons(recip(a__sqr(a__sqr(mark(X'')))), terms(s(sqr(X'')))) [2] a__terms(add(X1', X2')) -> cons(recip(a__sqr(a__add(mark(X1'), mark(X2')))), terms(s(add(X1', X2')))) [2] a__terms(dbl(X3)) -> cons(recip(a__sqr(a__dbl(mark(X3)))), terms(s(dbl(X3)))) [2] a__terms(first(X1'', X2'')) -> cons(recip(a__sqr(a__first(mark(X1''), mark(X2'')))), terms(s(first(X1'', X2'')))) [2] a__terms(cons(X11, X21)) -> cons(recip(a__sqr(cons(mark(X11), X21))), terms(s(cons(X11, X21)))) [2] a__terms(recip(X4)) -> cons(recip(a__sqr(recip(mark(X4)))), terms(s(recip(X4)))) [2] a__terms(s(X5)) -> cons(recip(a__sqr(s(X5))), terms(s(s(X5)))) [2] a__terms(0) -> cons(recip(a__sqr(0)), terms(s(0))) [2] a__terms(nil) -> cons(recip(a__sqr(nil)), terms(s(nil))) [2] a__sqr(0) -> 0 [1] a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) [1] a__dbl(0) -> 0 [1] a__dbl(s(X)) -> s(s(dbl(X))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(add(X, Y)) [1] a__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] mark(terms(terms(X6))) -> a__terms(a__terms(mark(X6))) [2] mark(terms(sqr(X7))) -> a__terms(a__sqr(mark(X7))) [2] mark(terms(add(X12, X22))) -> a__terms(a__add(mark(X12), mark(X22))) [2] mark(terms(dbl(X8))) -> a__terms(a__dbl(mark(X8))) [2] mark(terms(first(X13, X23))) -> a__terms(a__first(mark(X13), mark(X23))) [2] mark(terms(cons(X14, X24))) -> a__terms(cons(mark(X14), X24)) [2] mark(terms(recip(X9))) -> a__terms(recip(mark(X9))) [2] mark(terms(s(X10))) -> a__terms(s(X10)) [2] mark(terms(0)) -> a__terms(0) [2] mark(terms(nil)) -> a__terms(nil) [2] mark(sqr(terms(X15))) -> a__sqr(a__terms(mark(X15))) [2] mark(sqr(sqr(X16))) -> a__sqr(a__sqr(mark(X16))) [2] mark(sqr(add(X17, X25))) -> a__sqr(a__add(mark(X17), mark(X25))) [2] mark(sqr(dbl(X18))) -> a__sqr(a__dbl(mark(X18))) [2] mark(sqr(first(X19, X26))) -> a__sqr(a__first(mark(X19), mark(X26))) [2] mark(sqr(cons(X110, X27))) -> a__sqr(cons(mark(X110), X27)) [2] mark(sqr(recip(X20))) -> a__sqr(recip(mark(X20))) [2] mark(sqr(s(X28))) -> a__sqr(s(X28)) [2] mark(sqr(0)) -> a__sqr(0) [2] mark(sqr(nil)) -> a__sqr(nil) [2] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(dbl(terms(X84))) -> a__dbl(a__terms(mark(X84))) [2] mark(dbl(sqr(X85))) -> a__dbl(a__sqr(mark(X85))) [2] mark(dbl(add(X144, X243))) -> a__dbl(a__add(mark(X144), mark(X243))) [2] mark(dbl(dbl(X86))) -> a__dbl(a__dbl(mark(X86))) [2] mark(dbl(first(X145, X244))) -> a__dbl(a__first(mark(X145), mark(X244))) [2] mark(dbl(cons(X146, X245))) -> a__dbl(cons(mark(X146), X245)) [2] mark(dbl(recip(X87))) -> a__dbl(recip(mark(X87))) [2] mark(dbl(s(X88))) -> a__dbl(s(X88)) [2] mark(dbl(0)) -> a__dbl(0) [2] mark(dbl(nil)) -> a__dbl(nil) [2] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(X) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] a__terms(X) -> terms(X) [1] a__sqr(X) -> sqr(X) [1] a__add(X1, X2) -> add(X1, X2) [1] a__dbl(X) -> dbl(X) [1] a__first(X1, X2) -> first(X1, X2) [1] The TRS has the following type information: a__terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first cons :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first recip :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first mark :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first s :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first 0 :: recip:s:terms:cons:0:sqr:dbl:add:nil:first add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first nil :: recip:s:terms:cons:0:sqr:dbl:add:nil:first first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first Rewrite Strategy: INNERMOST ---------------------------------------- (25) 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 nil => 1 ---------------------------------------- (26) 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 + (1 + X + 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__dbl(z) -{ 1 }-> 0 :|: z = 0 a__dbl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__dbl(z) -{ 1 }-> 1 + (1 + (1 + X)) :|: z = 1 + X, X >= 0 a__first(z, z') -{ 1 }-> 1 :|: z' = X, X >= 0, z = 0 a__first(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + X + Z) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z a__sqr(z) -{ 1 }-> 0 :|: z = 0 a__sqr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__sqr(z) -{ 1 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z = 1 + X, X >= 0 a__terms(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__terms(mark(X')))) + (1 + (1 + (1 + X'))) :|: X' >= 0, z = 1 + X' a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__sqr(mark(X'')))) + (1 + (1 + (1 + X''))) :|: z = 1 + X'', X'' >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__first(mark(X1''), mark(X2'')))) + (1 + (1 + (1 + X1'' + X2''))) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__dbl(mark(X3)))) + (1 + (1 + (1 + X3))) :|: z = 1 + X3, X3 >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__add(mark(X1'), mark(X2')))) + (1 + (1 + (1 + X1' + X2'))) :|: X2' >= 0, X1' >= 0, z = 1 + X1' + X2' a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1)) + (1 + (1 + 1)) :|: z = 1 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(0)) + (1 + (1 + 0)) :|: z = 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + X5)) + (1 + (1 + (1 + X5))) :|: X5 >= 0, z = 1 + X5 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(X4))) + (1 + (1 + (1 + X4))) :|: z = 1 + X4, X4 >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(X11) + X21)) + (1 + (1 + (1 + X11 + X21))) :|: X11 >= 0, X21 >= 0, z = 1 + X11 + X21 mark(z) -{ 2 }-> a__terms(a__terms(mark(X6))) :|: X6 >= 0, z = 1 + (1 + X6) mark(z) -{ 2 }-> a__terms(a__sqr(mark(X7))) :|: X7 >= 0, z = 1 + (1 + X7) mark(z) -{ 2 }-> a__terms(a__first(mark(X13), mark(X23))) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0 mark(z) -{ 2 }-> a__terms(a__dbl(mark(X8))) :|: X8 >= 0, z = 1 + (1 + X8) mark(z) -{ 2 }-> a__terms(a__add(mark(X12), mark(X22))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) mark(z) -{ 2 }-> a__terms(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__terms(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__terms(1 + X10) :|: z = 1 + (1 + X10), X10 >= 0 mark(z) -{ 2 }-> a__terms(1 + mark(X9)) :|: X9 >= 0, z = 1 + (1 + X9) mark(z) -{ 2 }-> a__terms(1 + mark(X14) + X24) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0 mark(z) -{ 2 }-> a__sqr(a__terms(mark(X15))) :|: z = 1 + (1 + X15), X15 >= 0 mark(z) -{ 2 }-> a__sqr(a__sqr(mark(X16))) :|: X16 >= 0, z = 1 + (1 + X16) mark(z) -{ 2 }-> a__sqr(a__first(mark(X19), mark(X26))) :|: z = 1 + (1 + X19 + X26), X26 >= 0, X19 >= 0 mark(z) -{ 2 }-> a__sqr(a__dbl(mark(X18))) :|: X18 >= 0, z = 1 + (1 + X18) mark(z) -{ 2 }-> a__sqr(a__add(mark(X17), mark(X25))) :|: X17 >= 0, z = 1 + (1 + X17 + X25), X25 >= 0 mark(z) -{ 2 }-> a__sqr(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__sqr(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__sqr(1 + X28) :|: X28 >= 0, z = 1 + (1 + X28) mark(z) -{ 2 }-> a__sqr(1 + mark(X20)) :|: z = 1 + (1 + X20), X20 >= 0 mark(z) -{ 2 }-> a__sqr(1 + mark(X110) + X27) :|: X110 >= 0, X27 >= 0, z = 1 + (1 + X110 + X27) mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__dbl(a__terms(mark(X84))) :|: z = 1 + (1 + X84), X84 >= 0 mark(z) -{ 2 }-> a__dbl(a__sqr(mark(X85))) :|: z = 1 + (1 + X85), X85 >= 0 mark(z) -{ 2 }-> a__dbl(a__first(mark(X145), mark(X244))) :|: X244 >= 0, z = 1 + (1 + X145 + X244), X145 >= 0 mark(z) -{ 2 }-> a__dbl(a__dbl(mark(X86))) :|: z = 1 + (1 + X86), X86 >= 0 mark(z) -{ 2 }-> a__dbl(a__add(mark(X144), mark(X243))) :|: X243 >= 0, X144 >= 0, z = 1 + (1 + X144 + X243) mark(z) -{ 2 }-> a__dbl(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__dbl(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__dbl(1 + X88) :|: X88 >= 0, z = 1 + (1 + X88) mark(z) -{ 2 }-> a__dbl(1 + mark(X87)) :|: X87 >= 0, z = 1 + (1 + X87) mark(z) -{ 2 }-> a__dbl(1 + mark(X146) + X245) :|: X146 >= 0, X245 >= 0, z = 1 + (1 + X146 + X245) mark(z) -{ 1 }-> a__add(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + X :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (27) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__sqr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__sqr(z) -{ 1 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z = 1 + X, X >= 0 a__sqr(z) -{ 1 }-> 0 :|: z = 0 a__dbl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__dbl(z) -{ 1 }-> 1 + (1 + (1 + X)) :|: z = 1 + X, X >= 0 a__dbl(z) -{ 1 }-> 0 :|: z = 0 ---------------------------------------- (28) 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 + (1 + X + 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__dbl(z) -{ 1 }-> 0 :|: z = 0 a__dbl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__dbl(z) -{ 1 }-> 1 + (1 + (1 + X)) :|: z = 1 + X, X >= 0 a__first(z, z') -{ 1 }-> 1 :|: z' = X, X >= 0, z = 0 a__first(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + X + Z) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z a__sqr(z) -{ 1 }-> 0 :|: z = 0 a__sqr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__sqr(z) -{ 1 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z = 1 + X, X >= 0 a__terms(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__terms(mark(X')))) + (1 + (1 + (1 + X'))) :|: X' >= 0, z = 1 + X' a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__sqr(mark(X'')))) + (1 + (1 + (1 + X''))) :|: z = 1 + X'', X'' >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__first(mark(X1''), mark(X2'')))) + (1 + (1 + (1 + X1'' + X2''))) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__dbl(mark(X3)))) + (1 + (1 + (1 + X3))) :|: z = 1 + X3, X3 >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__add(mark(X1'), mark(X2')))) + (1 + (1 + (1 + X1' + X2'))) :|: X2' >= 0, X1' >= 0, z = 1 + X1' + X2' a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(X4))) + (1 + (1 + (1 + X4))) :|: z = 1 + X4, X4 >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(X11) + X21)) + (1 + (1 + (1 + X11 + X21))) :|: X11 >= 0, X21 >= 0, z = 1 + X11 + X21 a__terms(z) -{ 3 }-> 1 + (1 + 0) + (1 + (1 + 0)) :|: z = 0, 0 = 0 a__terms(z) -{ 3 }-> 1 + (1 + (1 + X)) + (1 + (1 + 1)) :|: z = 1, X >= 0, 1 = X a__terms(z) -{ 3 }-> 1 + (1 + (1 + X)) + (1 + (1 + 0)) :|: z = 0, X >= 0, 0 = X a__terms(z) -{ 3 }-> 1 + (1 + (1 + X)) + (1 + (1 + (1 + X5))) :|: X5 >= 0, z = 1 + X5, X >= 0, 1 + X5 = X a__terms(z) -{ 3 }-> 1 + (1 + (1 + (1 + (1 + X) + (1 + X)))) + (1 + (1 + 1)) :|: z = 1, 1 = 1 + X, X >= 0 a__terms(z) -{ 3 }-> 1 + (1 + (1 + (1 + (1 + X) + (1 + X)))) + (1 + (1 + (1 + X5))) :|: X5 >= 0, z = 1 + X5, 1 + X5 = 1 + X, X >= 0 mark(z) -{ 2 }-> a__terms(a__terms(mark(X6))) :|: X6 >= 0, z = 1 + (1 + X6) mark(z) -{ 2 }-> a__terms(a__sqr(mark(X7))) :|: X7 >= 0, z = 1 + (1 + X7) mark(z) -{ 2 }-> a__terms(a__first(mark(X13), mark(X23))) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0 mark(z) -{ 2 }-> a__terms(a__dbl(mark(X8))) :|: X8 >= 0, z = 1 + (1 + X8) mark(z) -{ 2 }-> a__terms(a__add(mark(X12), mark(X22))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) mark(z) -{ 2 }-> a__terms(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__terms(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__terms(1 + X10) :|: z = 1 + (1 + X10), X10 >= 0 mark(z) -{ 2 }-> a__terms(1 + mark(X9)) :|: X9 >= 0, z = 1 + (1 + X9) mark(z) -{ 2 }-> a__terms(1 + mark(X14) + X24) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0 mark(z) -{ 2 }-> a__sqr(a__terms(mark(X15))) :|: z = 1 + (1 + X15), X15 >= 0 mark(z) -{ 2 }-> a__sqr(a__sqr(mark(X16))) :|: X16 >= 0, z = 1 + (1 + X16) mark(z) -{ 2 }-> a__sqr(a__first(mark(X19), mark(X26))) :|: z = 1 + (1 + X19 + X26), X26 >= 0, X19 >= 0 mark(z) -{ 2 }-> a__sqr(a__dbl(mark(X18))) :|: X18 >= 0, z = 1 + (1 + X18) mark(z) -{ 2 }-> a__sqr(a__add(mark(X17), mark(X25))) :|: X17 >= 0, z = 1 + (1 + X17 + X25), X25 >= 0 mark(z) -{ 2 }-> a__sqr(1 + mark(X20)) :|: z = 1 + (1 + X20), X20 >= 0 mark(z) -{ 2 }-> a__sqr(1 + mark(X110) + X27) :|: X110 >= 0, X27 >= 0, z = 1 + (1 + X110 + X27) mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__dbl(a__terms(mark(X84))) :|: z = 1 + (1 + X84), X84 >= 0 mark(z) -{ 2 }-> a__dbl(a__sqr(mark(X85))) :|: z = 1 + (1 + X85), X85 >= 0 mark(z) -{ 2 }-> a__dbl(a__first(mark(X145), mark(X244))) :|: X244 >= 0, z = 1 + (1 + X145 + X244), X145 >= 0 mark(z) -{ 2 }-> a__dbl(a__dbl(mark(X86))) :|: z = 1 + (1 + X86), X86 >= 0 mark(z) -{ 2 }-> a__dbl(a__add(mark(X144), mark(X243))) :|: X243 >= 0, X144 >= 0, z = 1 + (1 + X144 + X243) mark(z) -{ 2 }-> a__dbl(1 + mark(X87)) :|: X87 >= 0, z = 1 + (1 + X87) mark(z) -{ 2 }-> a__dbl(1 + mark(X146) + X245) :|: X146 >= 0, X245 >= 0, z = 1 + (1 + X146 + X245) mark(z) -{ 1 }-> a__add(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 3 }-> 0 :|: z = 1 + 0, 0 = 0 mark(z) -{ 1 }-> 1 + X :|: z = 1 + X, X >= 0 mark(z) -{ 3 }-> 1 + X :|: X28 >= 0, z = 1 + (1 + X28), X >= 0, 1 + X28 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X mark(z) -{ 3 }-> 1 + X :|: X88 >= 0, z = 1 + (1 + X88), X >= 0, 1 + X88 = X mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 3 }-> 1 + (1 + (1 + X)) :|: X88 >= 0, z = 1 + (1 + X88), 1 + X88 = 1 + X, X >= 0 mark(z) -{ 3 }-> 1 + (1 + (1 + X)) :|: z = 1 + 1, 1 = 1 + X, X >= 0 mark(z) -{ 3 }-> 1 + (1 + (1 + X) + (1 + X)) :|: X28 >= 0, z = 1 + (1 + X28), 1 + X28 = 1 + X, X >= 0 mark(z) -{ 3 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z = 1 + 1, 1 = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (29) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (30) 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 + (1 + (z - 1) + z') :|: z' >= 0, z - 1 >= 0 a__add(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__dbl(z) -{ 1 }-> 0 :|: z = 0 a__dbl(z) -{ 1 }-> 1 + z :|: z >= 0 a__dbl(z) -{ 1 }-> 1 + (1 + (1 + (z - 1))) :|: z - 1 >= 0 a__first(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0 a__first(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + (z - 1) + Z) :|: Z >= 0, Y >= 0, z - 1 >= 0, z' = 1 + Y + Z a__sqr(z) -{ 1 }-> 0 :|: z = 0 a__sqr(z) -{ 1 }-> 1 + z :|: z >= 0 a__sqr(z) -{ 1 }-> 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) :|: z - 1 >= 0 a__terms(z) -{ 1 }-> 1 + z :|: z >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__terms(mark(z - 1)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__sqr(mark(z - 1)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__first(mark(X1''), mark(X2'')))) + (1 + (1 + (1 + X1'' + X2''))) :|: X1'' >= 0, z = 1 + X1'' + X2'', X2'' >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__dbl(mark(z - 1)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(a__add(mark(X1'), mark(X2')))) + (1 + (1 + (1 + X1' + X2'))) :|: X2' >= 0, X1' >= 0, z = 1 + X1' + X2' a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(z - 1))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0 a__terms(z) -{ 2 }-> 1 + (1 + a__sqr(1 + mark(X11) + X21)) + (1 + (1 + (1 + X11 + X21))) :|: X11 >= 0, X21 >= 0, z = 1 + X11 + X21 a__terms(z) -{ 3 }-> 1 + (1 + 0) + (1 + (1 + 0)) :|: z = 0, 0 = 0 a__terms(z) -{ 3 }-> 1 + (1 + (1 + X)) + (1 + (1 + 1)) :|: z = 1, X >= 0, 1 = X a__terms(z) -{ 3 }-> 1 + (1 + (1 + X)) + (1 + (1 + 0)) :|: z = 0, X >= 0, 0 = X a__terms(z) -{ 3 }-> 1 + (1 + (1 + X)) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0, X >= 0, 1 + (z - 1) = X a__terms(z) -{ 3 }-> 1 + (1 + (1 + (1 + (1 + X) + (1 + X)))) + (1 + (1 + 1)) :|: z = 1, 1 = 1 + X, X >= 0 a__terms(z) -{ 3 }-> 1 + (1 + (1 + (1 + (1 + X) + (1 + X)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0, 1 + (z - 1) = 1 + X, X >= 0 mark(z) -{ 2 }-> a__terms(a__terms(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__terms(a__sqr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__terms(a__first(mark(X13), mark(X23))) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0 mark(z) -{ 2 }-> a__terms(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__terms(a__add(mark(X12), mark(X22))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) mark(z) -{ 2 }-> a__terms(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__terms(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__terms(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__terms(1 + (z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__terms(1 + mark(X14) + X24) :|: z = 1 + (1 + X14 + X24), X14 >= 0, X24 >= 0 mark(z) -{ 2 }-> a__sqr(a__terms(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__sqr(a__sqr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__sqr(a__first(mark(X19), mark(X26))) :|: z = 1 + (1 + X19 + X26), X26 >= 0, X19 >= 0 mark(z) -{ 2 }-> a__sqr(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__sqr(a__add(mark(X17), mark(X25))) :|: X17 >= 0, z = 1 + (1 + X17 + X25), X25 >= 0 mark(z) -{ 2 }-> a__sqr(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__sqr(1 + mark(X110) + X27) :|: X110 >= 0, X27 >= 0, z = 1 + (1 + X110 + X27) mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__dbl(a__terms(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__dbl(a__sqr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__dbl(a__first(mark(X145), mark(X244))) :|: X244 >= 0, z = 1 + (1 + X145 + X244), X145 >= 0 mark(z) -{ 2 }-> a__dbl(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__dbl(a__add(mark(X144), mark(X243))) :|: X243 >= 0, X144 >= 0, z = 1 + (1 + X144 + X243) mark(z) -{ 2 }-> a__dbl(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__dbl(1 + mark(X146) + X245) :|: X146 >= 0, X245 >= 0, z = 1 + (1 + X146 + X245) mark(z) -{ 1 }-> a__add(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 3 }-> 0 :|: z = 1 + 0, 0 = 0 mark(z) -{ 3 }-> 1 + X :|: z - 2 >= 0, X >= 0, 1 + (z - 2) = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0 mark(z) -{ 3 }-> 1 + (1 + (1 + X)) :|: z - 2 >= 0, 1 + (z - 2) = 1 + X, X >= 0 mark(z) -{ 3 }-> 1 + (1 + (1 + X)) :|: z = 1 + 1, 1 = 1 + X, X >= 0 mark(z) -{ 3 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z - 2 >= 0, 1 + (z - 2) = 1 + X, X >= 0 mark(z) -{ 3 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z = 1 + 1, 1 = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (31) 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 ---------------------------------------- (32) 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__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N))) [1] a__sqr(0) -> 0 [1] a__sqr(s(X)) -> s(add(sqr(X), dbl(X))) [1] a__dbl(0) -> 0 [1] a__dbl(s(X)) -> s(s(dbl(X))) [1] a__add(0, X) -> mark(X) [1] a__add(s(X), Y) -> s(add(X, Y)) [1] a__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] mark(terms(X)) -> a__terms(mark(X)) [1] mark(sqr(X)) -> a__sqr(mark(X)) [1] mark(add(X1, X2)) -> a__add(mark(X1), mark(X2)) [1] mark(dbl(X)) -> a__dbl(mark(X)) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(recip(X)) -> recip(mark(X)) [1] mark(s(X)) -> s(X) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] a__terms(X) -> terms(X) [1] a__sqr(X) -> sqr(X) [1] a__add(X1, X2) -> add(X1, X2) [1] a__dbl(X) -> dbl(X) [1] a__first(X1, X2) -> first(X1, X2) [1] The TRS has the following type information: a__terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first cons :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first recip :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first mark :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first terms :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first s :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first 0 :: recip:s:terms:cons:0:sqr:dbl:add:nil:first add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first sqr :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__dbl :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__add :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first a__first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first nil :: recip:s:terms:cons:0:sqr:dbl:add:nil:first first :: recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first -> recip:s:terms:cons:0:sqr:dbl:add:nil:first Rewrite Strategy: INNERMOST ---------------------------------------- (33) 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 nil => 1 ---------------------------------------- (34) 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 + (1 + X + 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__dbl(z) -{ 1 }-> 0 :|: z = 0 a__dbl(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__dbl(z) -{ 1 }-> 1 + (1 + (1 + X)) :|: z = 1 + X, X >= 0 a__first(z, z') -{ 1 }-> 1 :|: z' = X, X >= 0, z = 0 a__first(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + X + Z) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z a__sqr(z) -{ 1 }-> 0 :|: z = 0 a__sqr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__sqr(z) -{ 1 }-> 1 + (1 + (1 + X) + (1 + X)) :|: z = 1 + X, X >= 0 a__terms(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__terms(z) -{ 1 }-> 1 + (1 + a__sqr(mark(N))) + (1 + (1 + N)) :|: z = N, N >= 0 mark(z) -{ 1 }-> a__terms(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__sqr(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__dbl(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 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + X :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (35) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0) -> c2 A__SQR(s(z0)) -> c3 A__SQR(z0) -> c4 A__DBL(0) -> c5 A__DBL(s(z0)) -> c6 A__DBL(z0) -> c7 A__ADD(0, z0) -> c8(MARK(z0)) A__ADD(s(z0), z1) -> c9 A__ADD(z0, z1) -> c10 A__FIRST(0, z0) -> c11 A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) A__FIRST(z0, z1) -> c13 MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) MARK(s(z0)) -> c23 MARK(0) -> c24 MARK(nil) -> c25 S tuples: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__TERMS(z0) -> c1 A__SQR(0) -> c2 A__SQR(s(z0)) -> c3 A__SQR(z0) -> c4 A__DBL(0) -> c5 A__DBL(s(z0)) -> c6 A__DBL(z0) -> c7 A__ADD(0, z0) -> c8(MARK(z0)) A__ADD(s(z0), z1) -> c9 A__ADD(z0, z1) -> c10 A__FIRST(0, z0) -> c11 A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) A__FIRST(z0, z1) -> c13 MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) MARK(s(z0)) -> c23 MARK(0) -> c24 MARK(nil) -> c25 K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__TERMS_1, A__SQR_1, A__DBL_1, A__ADD_2, A__FIRST_2, MARK_1 Compound Symbols: c_2, c1, c2, c3, c4, c5, c6, c7, c8_1, c9, c10, c11, c12_1, c13, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c20_2, c21_1, c22_1, c23, c24, c25 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 14 trailing nodes: A__DBL(s(z0)) -> c6 A__TERMS(z0) -> c1 A__SQR(s(z0)) -> c3 A__FIRST(z0, z1) -> c13 A__DBL(z0) -> c7 A__DBL(0) -> c5 A__FIRST(0, z0) -> c11 A__ADD(s(z0), z1) -> c9 A__SQR(0) -> c2 MARK(nil) -> c25 MARK(0) -> c24 A__ADD(z0, z1) -> c10 MARK(s(z0)) -> c23 A__SQR(z0) -> c4 ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) S tuples: A__TERMS(z0) -> c(A__SQR(mark(z0)), MARK(z0)) A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(sqr(z0)) -> c15(A__SQR(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(dbl(z0)) -> c18(A__DBL(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__TERMS_1, A__ADD_2, A__FIRST_2, MARK_1 Compound Symbols: c_2, c8_1, c12_1, c14_2, c15_2, c16_2, c17_2, c18_2, c19_2, c20_2, c21_1, c22_1 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c16_2, c17_2, c19_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1 ---------------------------------------- (41) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (42) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) The (relative) TRS S consists of the following rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Rewrite Strategy: INNERMOST ---------------------------------------- (43) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (44) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (45) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (46) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__ADD(0, z0) -> c8(MARK(z0)) [1] A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) [1] MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) [1] MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) [1] MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c21(MARK(z0)) [1] MARK(recip(z0)) -> c22(MARK(z0)) [1] A__TERMS(z0) -> c(MARK(z0)) [1] MARK(sqr(z0)) -> c15(MARK(z0)) [1] MARK(dbl(z0)) -> c18(MARK(z0)) [1] a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) [0] a__terms(z0) -> terms(z0) [0] a__sqr(0) -> 0 [0] a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) [0] a__sqr(z0) -> sqr(z0) [0] a__dbl(0) -> 0 [0] a__dbl(s(z0)) -> s(s(dbl(z0))) [0] a__dbl(z0) -> dbl(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(add(z0, z1)) [0] a__add(z0, z1) -> add(z0, z1) [0] a__first(0, z0) -> nil [0] a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) [0] a__first(z0, z1) -> first(z0, z1) [0] mark(terms(z0)) -> a__terms(mark(z0)) [0] mark(sqr(z0)) -> a__sqr(mark(z0)) [0] mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) [0] mark(dbl(z0)) -> a__dbl(mark(z0)) [0] mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(recip(z0)) -> recip(mark(z0)) [0] mark(s(z0)) -> s(z0) [0] mark(0) -> 0 [0] mark(nil) -> nil [0] Rewrite Strategy: INNERMOST ---------------------------------------- (47) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (48) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__ADD(0, z0) -> c8(MARK(z0)) [1] A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) [1] MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) [1] MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) [1] MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c21(MARK(z0)) [1] MARK(recip(z0)) -> c22(MARK(z0)) [1] A__TERMS(z0) -> c(MARK(z0)) [1] MARK(sqr(z0)) -> c15(MARK(z0)) [1] MARK(dbl(z0)) -> c18(MARK(z0)) [1] a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) [0] a__terms(z0) -> terms(z0) [0] a__sqr(0) -> 0 [0] a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) [0] a__sqr(z0) -> sqr(z0) [0] a__dbl(0) -> 0 [0] a__dbl(s(z0)) -> s(s(dbl(z0))) [0] a__dbl(z0) -> dbl(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(add(z0, z1)) [0] a__add(z0, z1) -> add(z0, z1) [0] a__first(0, z0) -> nil [0] a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) [0] a__first(z0, z1) -> first(z0, z1) [0] mark(terms(z0)) -> a__terms(mark(z0)) [0] mark(sqr(z0)) -> a__sqr(mark(z0)) [0] mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) [0] mark(dbl(z0)) -> a__dbl(mark(z0)) [0] mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(recip(z0)) -> recip(mark(z0)) [0] mark(s(z0)) -> s(z0) [0] mark(0) -> 0 [0] mark(nil) -> nil [0] The TRS has the following type information: A__ADD :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> c8 0 :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil c8 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c8 MARK :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> c14:c16:c17:c19:c20:c21:c22:c15:c18 A__FIRST :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> c12 s :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil cons :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil c12 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c12 terms :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil c14 :: c -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 A__TERMS :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> c mark :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil add :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil c16 :: c8 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 c17 :: c8 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 first :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil c19 :: c12 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 c20 :: c12 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 c21 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 recip :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil c22 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 c :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c sqr :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil c15 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 dbl :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil c18 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 a__terms :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil a__sqr :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil a__dbl :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil a__add :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil a__first :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil nil :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil Rewrite Strategy: INNERMOST ---------------------------------------- (49) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: A__ADD_2 A__FIRST_2 MARK_1 A__TERMS_1 (c) The following functions are completely defined: a__terms_1 a__sqr_1 a__dbl_1 a__add_2 a__first_2 mark_1 Due to the following rules being added: a__terms(v0) -> null_a__terms [0] a__sqr(v0) -> null_a__sqr [0] a__dbl(v0) -> null_a__dbl [0] a__add(v0, v1) -> null_a__add [0] a__first(v0, v1) -> null_a__first [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__terms, null_a__sqr, null_a__dbl, null_a__add, null_a__first, null_mark, const, const1, const2, const3 ---------------------------------------- (50) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__ADD(0, z0) -> c8(MARK(z0)) [1] A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) [1] MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) [1] MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) [1] MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c21(MARK(z0)) [1] MARK(recip(z0)) -> c22(MARK(z0)) [1] A__TERMS(z0) -> c(MARK(z0)) [1] MARK(sqr(z0)) -> c15(MARK(z0)) [1] MARK(dbl(z0)) -> c18(MARK(z0)) [1] a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) [0] a__terms(z0) -> terms(z0) [0] a__sqr(0) -> 0 [0] a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) [0] a__sqr(z0) -> sqr(z0) [0] a__dbl(0) -> 0 [0] a__dbl(s(z0)) -> s(s(dbl(z0))) [0] a__dbl(z0) -> dbl(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(add(z0, z1)) [0] a__add(z0, z1) -> add(z0, z1) [0] a__first(0, z0) -> nil [0] a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) [0] a__first(z0, z1) -> first(z0, z1) [0] mark(terms(z0)) -> a__terms(mark(z0)) [0] mark(sqr(z0)) -> a__sqr(mark(z0)) [0] mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) [0] mark(dbl(z0)) -> a__dbl(mark(z0)) [0] mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(recip(z0)) -> recip(mark(z0)) [0] mark(s(z0)) -> s(z0) [0] mark(0) -> 0 [0] mark(nil) -> nil [0] a__terms(v0) -> null_a__terms [0] a__sqr(v0) -> null_a__sqr [0] a__dbl(v0) -> null_a__dbl [0] a__add(v0, v1) -> null_a__add [0] a__first(v0, v1) -> null_a__first [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__ADD :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> c8 0 :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c8 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c8 MARK :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> c14:c16:c17:c19:c20:c21:c22:c15:c18 A__FIRST :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> c12 s :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark cons :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c12 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c12 terms :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c14 :: c -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 A__TERMS :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> c mark :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark add :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c16 :: c8 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 c17 :: c8 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 first :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c19 :: c12 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 c20 :: c12 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 c21 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 recip :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c22 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 c :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c sqr :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c15 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 dbl :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c18 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 a__terms :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark a__sqr :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark a__dbl :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark a__add :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark a__first :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark nil :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__terms :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__sqr :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__dbl :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__add :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__first :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_mark :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark const :: c8 const1 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 const2 :: c12 const3 :: c Rewrite Strategy: INNERMOST ---------------------------------------- (51) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (52) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__ADD(0, z0) -> c8(MARK(z0)) [1] A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) [1] MARK(terms(terms(z0'))) -> c14(A__TERMS(a__terms(mark(z0'))), MARK(terms(z0'))) [1] MARK(terms(sqr(z0''))) -> c14(A__TERMS(a__sqr(mark(z0''))), MARK(sqr(z0''))) [1] MARK(terms(add(z01, z1'))) -> c14(A__TERMS(a__add(mark(z01), mark(z1'))), MARK(add(z01, z1'))) [1] MARK(terms(dbl(z02))) -> c14(A__TERMS(a__dbl(mark(z02))), MARK(dbl(z02))) [1] MARK(terms(first(z03, z1''))) -> c14(A__TERMS(a__first(mark(z03), mark(z1''))), MARK(first(z03, z1''))) [1] MARK(terms(cons(z04, z11))) -> c14(A__TERMS(cons(mark(z04), z11)), MARK(cons(z04, z11))) [1] MARK(terms(recip(z05))) -> c14(A__TERMS(recip(mark(z05))), MARK(recip(z05))) [1] MARK(terms(s(z06))) -> c14(A__TERMS(s(z06)), MARK(s(z06))) [1] MARK(terms(0)) -> c14(A__TERMS(0), MARK(0)) [1] MARK(terms(nil)) -> c14(A__TERMS(nil), MARK(nil)) [1] MARK(terms(z0)) -> c14(A__TERMS(null_mark), MARK(z0)) [1] MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) [1] MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c21(MARK(z0)) [1] MARK(recip(z0)) -> c22(MARK(z0)) [1] A__TERMS(z0) -> c(MARK(z0)) [1] MARK(sqr(z0)) -> c15(MARK(z0)) [1] MARK(dbl(z0)) -> c18(MARK(z0)) [1] a__terms(terms(z0391)) -> cons(recip(a__sqr(a__terms(mark(z0391)))), terms(s(terms(z0391)))) [0] a__terms(sqr(z0392)) -> cons(recip(a__sqr(a__sqr(mark(z0392)))), terms(s(sqr(z0392)))) [0] a__terms(add(z0393, z1146)) -> cons(recip(a__sqr(a__add(mark(z0393), mark(z1146)))), terms(s(add(z0393, z1146)))) [0] a__terms(dbl(z0394)) -> cons(recip(a__sqr(a__dbl(mark(z0394)))), terms(s(dbl(z0394)))) [0] a__terms(first(z0395, z1147)) -> cons(recip(a__sqr(a__first(mark(z0395), mark(z1147)))), terms(s(first(z0395, z1147)))) [0] a__terms(cons(z0396, z1148)) -> cons(recip(a__sqr(cons(mark(z0396), z1148))), terms(s(cons(z0396, z1148)))) [0] a__terms(recip(z0397)) -> cons(recip(a__sqr(recip(mark(z0397)))), terms(s(recip(z0397)))) [0] a__terms(s(z0398)) -> cons(recip(a__sqr(s(z0398))), terms(s(s(z0398)))) [0] a__terms(0) -> cons(recip(a__sqr(0)), terms(s(0))) [0] a__terms(nil) -> cons(recip(a__sqr(nil)), terms(s(nil))) [0] a__terms(z0) -> cons(recip(a__sqr(null_mark)), terms(s(z0))) [0] a__terms(z0) -> terms(z0) [0] a__sqr(0) -> 0 [0] a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) [0] a__sqr(z0) -> sqr(z0) [0] a__dbl(0) -> 0 [0] a__dbl(s(z0)) -> s(s(dbl(z0))) [0] a__dbl(z0) -> dbl(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(add(z0, z1)) [0] a__add(z0, z1) -> add(z0, z1) [0] a__first(0, z0) -> nil [0] a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) [0] a__first(z0, z1) -> first(z0, z1) [0] mark(terms(terms(z0399))) -> a__terms(a__terms(mark(z0399))) [0] mark(terms(sqr(z0400))) -> a__terms(a__sqr(mark(z0400))) [0] mark(terms(add(z0401, z1149))) -> a__terms(a__add(mark(z0401), mark(z1149))) [0] mark(terms(dbl(z0402))) -> a__terms(a__dbl(mark(z0402))) [0] mark(terms(first(z0403, z1150))) -> a__terms(a__first(mark(z0403), mark(z1150))) [0] mark(terms(cons(z0404, z1151))) -> a__terms(cons(mark(z0404), z1151)) [0] mark(terms(recip(z0405))) -> a__terms(recip(mark(z0405))) [0] mark(terms(s(z0406))) -> a__terms(s(z0406)) [0] mark(terms(0)) -> a__terms(0) [0] mark(terms(nil)) -> a__terms(nil) [0] mark(terms(z0)) -> a__terms(null_mark) [0] mark(sqr(terms(z0407))) -> a__sqr(a__terms(mark(z0407))) [0] mark(sqr(sqr(z0408))) -> a__sqr(a__sqr(mark(z0408))) [0] mark(sqr(add(z0409, z1152))) -> a__sqr(a__add(mark(z0409), mark(z1152))) [0] mark(sqr(dbl(z0410))) -> a__sqr(a__dbl(mark(z0410))) [0] mark(sqr(first(z0411, z1153))) -> a__sqr(a__first(mark(z0411), mark(z1153))) [0] mark(sqr(cons(z0412, z1154))) -> a__sqr(cons(mark(z0412), z1154)) [0] mark(sqr(recip(z0413))) -> a__sqr(recip(mark(z0413))) [0] mark(sqr(s(z0414))) -> a__sqr(s(z0414)) [0] mark(sqr(0)) -> a__sqr(0) [0] mark(sqr(nil)) -> a__sqr(nil) [0] mark(sqr(z0)) -> a__sqr(null_mark) [0] mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) [0] mark(dbl(terms(z0511))) -> a__dbl(a__terms(mark(z0511))) [0] mark(dbl(sqr(z0512))) -> a__dbl(a__sqr(mark(z0512))) [0] mark(dbl(add(z0513, z1191))) -> a__dbl(a__add(mark(z0513), mark(z1191))) [0] mark(dbl(dbl(z0514))) -> a__dbl(a__dbl(mark(z0514))) [0] mark(dbl(first(z0515, z1192))) -> a__dbl(a__first(mark(z0515), mark(z1192))) [0] mark(dbl(cons(z0516, z1193))) -> a__dbl(cons(mark(z0516), z1193)) [0] mark(dbl(recip(z0517))) -> a__dbl(recip(mark(z0517))) [0] mark(dbl(s(z0518))) -> a__dbl(s(z0518)) [0] mark(dbl(0)) -> a__dbl(0) [0] mark(dbl(nil)) -> a__dbl(nil) [0] mark(dbl(z0)) -> a__dbl(null_mark) [0] mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(recip(z0)) -> recip(mark(z0)) [0] mark(s(z0)) -> s(z0) [0] mark(0) -> 0 [0] mark(nil) -> nil [0] a__terms(v0) -> null_a__terms [0] a__sqr(v0) -> null_a__sqr [0] a__dbl(v0) -> null_a__dbl [0] a__add(v0, v1) -> null_a__add [0] a__first(v0, v1) -> null_a__first [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__ADD :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> c8 0 :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c8 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c8 MARK :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> c14:c16:c17:c19:c20:c21:c22:c15:c18 A__FIRST :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> c12 s :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark cons :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c12 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c12 terms :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c14 :: c -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 A__TERMS :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> c mark :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark add :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c16 :: c8 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 c17 :: c8 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 first :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c19 :: c12 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 c20 :: c12 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 c21 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 recip :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c22 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 c :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c sqr :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c15 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 dbl :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c18 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 -> c14:c16:c17:c19:c20:c21:c22:c15:c18 a__terms :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark a__sqr :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark a__dbl :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark a__add :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark a__first :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark nil :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__terms :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__sqr :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__dbl :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__add :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__first :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_mark :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark const :: c8 const1 :: c14:c16:c17:c19:c20:c21:c22:c15:c18 const2 :: c12 const3 :: c Rewrite Strategy: INNERMOST ---------------------------------------- (53) 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 nil => 1 null_a__terms => 0 null_a__sqr => 0 null_a__dbl => 0 null_a__add => 0 null_a__first => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 ---------------------------------------- (54) Obligation: Complexity RNTS consisting of the following rules: A__ADD(z, z') -{ 1 }-> 1 + MARK(z0) :|: z0 >= 0, z = 0, z' = z0 A__FIRST(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__TERMS(z) -{ 1 }-> 1 + MARK(z0) :|: z = z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__terms(mark(z0'))) + MARK(1 + z0') :|: z = 1 + (1 + z0'), z0' >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__sqr(mark(z0''))) + MARK(1 + z0'') :|: z = 1 + (1 + z0''), z0'' >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__first(mark(z03), mark(z1''))) + MARK(1 + z03 + z1'') :|: z = 1 + (1 + z03 + z1''), z03 >= 0, z1'' >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__dbl(mark(z02))) + MARK(1 + z02) :|: z = 1 + (1 + z02), z02 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__add(mark(z01), mark(z1'))) + MARK(1 + z01 + z1') :|: z = 1 + (1 + z01 + z1'), z01 >= 0, z1' >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__TERMS(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__TERMS(1 + z06) + MARK(1 + z06) :|: z06 >= 0, z = 1 + (1 + z06) MARK(z) -{ 1 }-> 1 + A__TERMS(1 + mark(z05)) + MARK(1 + z05) :|: z05 >= 0, z = 1 + (1 + z05) MARK(z) -{ 1 }-> 1 + A__TERMS(1 + mark(z04) + z11) + MARK(1 + z04 + z11) :|: z04 >= 0, z = 1 + (1 + z04 + z11), z11 >= 0 MARK(z) -{ 1 }-> 1 + A__FIRST(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__FIRST(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__add(z, z') -{ 0 }-> mark(z0) :|: z0 >= 0, z = 0, z' = z0 a__add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__add(z, z') -{ 0 }-> 1 + (1 + z0 + z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 a__add(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__dbl(z) -{ 0 }-> 0 :|: z = 0 a__dbl(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__dbl(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + (1 + z0)) :|: z = 1 + z0, z0 >= 0 a__first(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0 a__first(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__first(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__first(z, z') -{ 0 }-> 1 + mark(z1) + (1 + z0 + z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__sqr(z) -{ 0 }-> 0 :|: z = 0 a__sqr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__sqr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__sqr(z) -{ 0 }-> 1 + (1 + (1 + z0) + (1 + z0)) :|: z = 1 + z0, z0 >= 0 a__terms(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__terms(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__terms(mark(z0391)))) + (1 + (1 + (1 + z0391))) :|: z = 1 + z0391, z0391 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__sqr(mark(z0392)))) + (1 + (1 + (1 + z0392))) :|: z = 1 + z0392, z0392 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__first(mark(z0395), mark(z1147)))) + (1 + (1 + (1 + z0395 + z1147))) :|: z1147 >= 0, z0395 >= 0, z = 1 + z0395 + z1147 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__dbl(mark(z0394)))) + (1 + (1 + (1 + z0394))) :|: z = 1 + z0394, z0394 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__add(mark(z0393), mark(z1146)))) + (1 + (1 + (1 + z0393 + z1146))) :|: z = 1 + z0393 + z1146, z1146 >= 0, z0393 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(1)) + (1 + (1 + 1)) :|: z = 1 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(0)) + (1 + (1 + z0)) :|: z = z0, z0 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(0)) + (1 + (1 + 0)) :|: z = 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(1 + z0398)) + (1 + (1 + (1 + z0398))) :|: z0398 >= 0, z = 1 + z0398 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(1 + mark(z0397))) + (1 + (1 + (1 + z0397))) :|: z0397 >= 0, z = 1 + z0397 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(1 + mark(z0396) + z1148)) + (1 + (1 + (1 + z0396 + z1148))) :|: z = 1 + z0396 + z1148, z0396 >= 0, z1148 >= 0 mark(z) -{ 0 }-> a__terms(a__terms(mark(z0399))) :|: z0399 >= 0, z = 1 + (1 + z0399) mark(z) -{ 0 }-> a__terms(a__sqr(mark(z0400))) :|: z = 1 + (1 + z0400), z0400 >= 0 mark(z) -{ 0 }-> a__terms(a__first(mark(z0403), mark(z1150))) :|: z0403 >= 0, z1150 >= 0, z = 1 + (1 + z0403 + z1150) mark(z) -{ 0 }-> a__terms(a__dbl(mark(z0402))) :|: z = 1 + (1 + z0402), z0402 >= 0 mark(z) -{ 0 }-> a__terms(a__add(mark(z0401), mark(z1149))) :|: z = 1 + (1 + z0401 + z1149), z0401 >= 0, z1149 >= 0 mark(z) -{ 0 }-> a__terms(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__terms(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__terms(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__terms(1 + z0406) :|: z = 1 + (1 + z0406), z0406 >= 0 mark(z) -{ 0 }-> a__terms(1 + mark(z0405)) :|: z0405 >= 0, z = 1 + (1 + z0405) mark(z) -{ 0 }-> a__terms(1 + mark(z0404) + z1151) :|: z1151 >= 0, z0404 >= 0, z = 1 + (1 + z0404 + z1151) mark(z) -{ 0 }-> a__sqr(a__terms(mark(z0407))) :|: z0407 >= 0, z = 1 + (1 + z0407) mark(z) -{ 0 }-> a__sqr(a__sqr(mark(z0408))) :|: z0408 >= 0, z = 1 + (1 + z0408) mark(z) -{ 0 }-> a__sqr(a__first(mark(z0411), mark(z1153))) :|: z = 1 + (1 + z0411 + z1153), z1153 >= 0, z0411 >= 0 mark(z) -{ 0 }-> a__sqr(a__dbl(mark(z0410))) :|: z = 1 + (1 + z0410), z0410 >= 0 mark(z) -{ 0 }-> a__sqr(a__add(mark(z0409), mark(z1152))) :|: z0409 >= 0, z = 1 + (1 + z0409 + z1152), z1152 >= 0 mark(z) -{ 0 }-> a__sqr(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__sqr(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__sqr(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__sqr(1 + z0414) :|: z = 1 + (1 + z0414), z0414 >= 0 mark(z) -{ 0 }-> a__sqr(1 + mark(z0413)) :|: z0413 >= 0, z = 1 + (1 + z0413) mark(z) -{ 0 }-> a__sqr(1 + mark(z0412) + z1154) :|: z1154 >= 0, z = 1 + (1 + z0412 + z1154), z0412 >= 0 mark(z) -{ 0 }-> a__first(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__dbl(a__terms(mark(z0511))) :|: z = 1 + (1 + z0511), z0511 >= 0 mark(z) -{ 0 }-> a__dbl(a__sqr(mark(z0512))) :|: z0512 >= 0, z = 1 + (1 + z0512) mark(z) -{ 0 }-> a__dbl(a__first(mark(z0515), mark(z1192))) :|: z0515 >= 0, z1192 >= 0, z = 1 + (1 + z0515 + z1192) mark(z) -{ 0 }-> a__dbl(a__dbl(mark(z0514))) :|: z = 1 + (1 + z0514), z0514 >= 0 mark(z) -{ 0 }-> a__dbl(a__add(mark(z0513), mark(z1191))) :|: z = 1 + (1 + z0513 + z1191), z1191 >= 0, z0513 >= 0 mark(z) -{ 0 }-> a__dbl(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__dbl(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__dbl(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__dbl(1 + z0518) :|: z = 1 + (1 + z0518), z0518 >= 0 mark(z) -{ 0 }-> a__dbl(1 + mark(z0517)) :|: z0517 >= 0, z = 1 + (1 + z0517) mark(z) -{ 0 }-> a__dbl(1 + mark(z0516) + z1193) :|: z1193 >= 0, z0516 >= 0, z = 1 + (1 + z0516 + z1193) mark(z) -{ 0 }-> a__add(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ---------------------------------------- (55) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__sqr(z) -{ 0 }-> 1 + (1 + (1 + z0) + (1 + z0)) :|: z = 1 + z0, z0 >= 0 a__sqr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__sqr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__sqr(z) -{ 0 }-> 0 :|: z = 0 a__dbl(z) -{ 0 }-> 0 :|: z = 0 a__dbl(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__dbl(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__dbl(z) -{ 0 }-> 1 + (1 + (1 + z0)) :|: z = 1 + z0, z0 >= 0 ---------------------------------------- (56) Obligation: Complexity RNTS consisting of the following rules: A__ADD(z, z') -{ 1 }-> 1 + MARK(z0) :|: z0 >= 0, z = 0, z' = z0 A__FIRST(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__TERMS(z) -{ 1 }-> 1 + MARK(z0) :|: z = z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__terms(mark(z0'))) + MARK(1 + z0') :|: z = 1 + (1 + z0'), z0' >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__sqr(mark(z0''))) + MARK(1 + z0'') :|: z = 1 + (1 + z0''), z0'' >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__first(mark(z03), mark(z1''))) + MARK(1 + z03 + z1'') :|: z = 1 + (1 + z03 + z1''), z03 >= 0, z1'' >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__dbl(mark(z02))) + MARK(1 + z02) :|: z = 1 + (1 + z02), z02 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__add(mark(z01), mark(z1'))) + MARK(1 + z01 + z1') :|: z = 1 + (1 + z01 + z1'), z01 >= 0, z1' >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__TERMS(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__TERMS(1 + z06) + MARK(1 + z06) :|: z06 >= 0, z = 1 + (1 + z06) MARK(z) -{ 1 }-> 1 + A__TERMS(1 + mark(z05)) + MARK(1 + z05) :|: z05 >= 0, z = 1 + (1 + z05) MARK(z) -{ 1 }-> 1 + A__TERMS(1 + mark(z04) + z11) + MARK(1 + z04 + z11) :|: z04 >= 0, z = 1 + (1 + z04 + z11), z11 >= 0 MARK(z) -{ 1 }-> 1 + A__FIRST(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__FIRST(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__add(z, z') -{ 0 }-> mark(z0) :|: z0 >= 0, z = 0, z' = z0 a__add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__add(z, z') -{ 0 }-> 1 + (1 + z0 + z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 a__add(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__dbl(z) -{ 0 }-> 0 :|: z = 0 a__dbl(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__dbl(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + (1 + z0)) :|: z = 1 + z0, z0 >= 0 a__first(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0 a__first(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__first(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__first(z, z') -{ 0 }-> 1 + mark(z1) + (1 + z0 + z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__sqr(z) -{ 0 }-> 0 :|: z = 0 a__sqr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__sqr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__sqr(z) -{ 0 }-> 1 + (1 + (1 + z0) + (1 + z0)) :|: z = 1 + z0, z0 >= 0 a__terms(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__terms(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__terms(mark(z0391)))) + (1 + (1 + (1 + z0391))) :|: z = 1 + z0391, z0391 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__sqr(mark(z0392)))) + (1 + (1 + (1 + z0392))) :|: z = 1 + z0392, z0392 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__first(mark(z0395), mark(z1147)))) + (1 + (1 + (1 + z0395 + z1147))) :|: z1147 >= 0, z0395 >= 0, z = 1 + z0395 + z1147 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__dbl(mark(z0394)))) + (1 + (1 + (1 + z0394))) :|: z = 1 + z0394, z0394 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__add(mark(z0393), mark(z1146)))) + (1 + (1 + (1 + z0393 + z1146))) :|: z = 1 + z0393 + z1146, z1146 >= 0, z0393 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(1 + mark(z0397))) + (1 + (1 + (1 + z0397))) :|: z0397 >= 0, z = 1 + z0397 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(1 + mark(z0396) + z1148)) + (1 + (1 + (1 + z0396 + z1148))) :|: z = 1 + z0396 + z1148, z0396 >= 0, z1148 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + 0) + (1 + (1 + z0)) :|: z = z0, z0 >= 0, v0 >= 0, 0 = v0 a__terms(z) -{ 0 }-> 1 + (1 + 0) + (1 + (1 + z0)) :|: z = z0, z0 >= 0, 0 = 0 a__terms(z) -{ 0 }-> 1 + (1 + 0) + (1 + (1 + 1)) :|: z = 1, v0 >= 0, 1 = v0 a__terms(z) -{ 0 }-> 1 + (1 + 0) + (1 + (1 + 0)) :|: z = 0, v0 >= 0, 0 = v0 a__terms(z) -{ 0 }-> 1 + (1 + 0) + (1 + (1 + 0)) :|: z = 0, 0 = 0 a__terms(z) -{ 0 }-> 1 + (1 + 0) + (1 + (1 + (1 + z0398))) :|: z0398 >= 0, z = 1 + z0398, v0 >= 0, 1 + z0398 = v0 a__terms(z) -{ 0 }-> 1 + (1 + (1 + z0)) + (1 + (1 + 1)) :|: z = 1, 1 = z0, z0 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + (1 + z0)) + (1 + (1 + 0)) :|: z = 0, 0 = z0, z0 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + (1 + z0)) + (1 + (1 + (1 + z0398))) :|: z0398 >= 0, z = 1 + z0398, 1 + z0398 = z0, z0 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + (1 + z0')) + (1 + (1 + z0)) :|: z = z0, z0 >= 0, 0 = z0', z0' >= 0 a__terms(z) -{ 0 }-> 1 + (1 + (1 + (1 + (1 + z0) + (1 + z0)))) + (1 + (1 + 1)) :|: z = 1, 1 = 1 + z0, z0 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + (1 + (1 + (1 + z0) + (1 + z0)))) + (1 + (1 + (1 + z0398))) :|: z0398 >= 0, z = 1 + z0398, 1 + z0398 = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__terms(a__terms(mark(z0399))) :|: z0399 >= 0, z = 1 + (1 + z0399) mark(z) -{ 0 }-> a__terms(a__sqr(mark(z0400))) :|: z = 1 + (1 + z0400), z0400 >= 0 mark(z) -{ 0 }-> a__terms(a__first(mark(z0403), mark(z1150))) :|: z0403 >= 0, z1150 >= 0, z = 1 + (1 + z0403 + z1150) mark(z) -{ 0 }-> a__terms(a__dbl(mark(z0402))) :|: z = 1 + (1 + z0402), z0402 >= 0 mark(z) -{ 0 }-> a__terms(a__add(mark(z0401), mark(z1149))) :|: z = 1 + (1 + z0401 + z1149), z0401 >= 0, z1149 >= 0 mark(z) -{ 0 }-> a__terms(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__terms(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__terms(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__terms(1 + z0406) :|: z = 1 + (1 + z0406), z0406 >= 0 mark(z) -{ 0 }-> a__terms(1 + mark(z0405)) :|: z0405 >= 0, z = 1 + (1 + z0405) mark(z) -{ 0 }-> a__terms(1 + mark(z0404) + z1151) :|: z1151 >= 0, z0404 >= 0, z = 1 + (1 + z0404 + z1151) mark(z) -{ 0 }-> a__sqr(a__terms(mark(z0407))) :|: z0407 >= 0, z = 1 + (1 + z0407) mark(z) -{ 0 }-> a__sqr(a__sqr(mark(z0408))) :|: z0408 >= 0, z = 1 + (1 + z0408) mark(z) -{ 0 }-> a__sqr(a__first(mark(z0411), mark(z1153))) :|: z = 1 + (1 + z0411 + z1153), z1153 >= 0, z0411 >= 0 mark(z) -{ 0 }-> a__sqr(a__dbl(mark(z0410))) :|: z = 1 + (1 + z0410), z0410 >= 0 mark(z) -{ 0 }-> a__sqr(a__add(mark(z0409), mark(z1152))) :|: z0409 >= 0, z = 1 + (1 + z0409 + z1152), z1152 >= 0 mark(z) -{ 0 }-> a__sqr(1 + mark(z0413)) :|: z0413 >= 0, z = 1 + (1 + z0413) mark(z) -{ 0 }-> a__sqr(1 + mark(z0412) + z1154) :|: z1154 >= 0, z = 1 + (1 + z0412 + z1154), z0412 >= 0 mark(z) -{ 0 }-> a__first(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__dbl(a__terms(mark(z0511))) :|: z = 1 + (1 + z0511), z0511 >= 0 mark(z) -{ 0 }-> a__dbl(a__sqr(mark(z0512))) :|: z0512 >= 0, z = 1 + (1 + z0512) mark(z) -{ 0 }-> a__dbl(a__first(mark(z0515), mark(z1192))) :|: z0515 >= 0, z1192 >= 0, z = 1 + (1 + z0515 + z1192) mark(z) -{ 0 }-> a__dbl(a__dbl(mark(z0514))) :|: z = 1 + (1 + z0514), z0514 >= 0 mark(z) -{ 0 }-> a__dbl(a__add(mark(z0513), mark(z1191))) :|: z = 1 + (1 + z0513 + z1191), z1191 >= 0, z0513 >= 0 mark(z) -{ 0 }-> a__dbl(1 + mark(z0517)) :|: z0517 >= 0, z = 1 + (1 + z0517) mark(z) -{ 0 }-> a__dbl(1 + mark(z0516) + z1193) :|: z1193 >= 0, z0516 >= 0, z = 1 + (1 + z0516 + z1193) mark(z) -{ 0 }-> a__add(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + (1 + z0414), z0414 >= 0, v0 >= 0, 1 + z0414 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 0, 0 = 0 mark(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, 0 = 0 mark(z) -{ 0 }-> 0 :|: z = 1 + (1 + z0518), z0518 >= 0, v0 >= 0, 1 + z0518 = v0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + (1 + z0414), z0414 >= 0, 1 + z0414 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 1, 1 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + (1 + z0518), z0518 >= 0, 1 + z0518 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, 0 = z0', z0' >= 0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + (1 + (1 + z0)) :|: z = 1 + (1 + z0518), z0518 >= 0, 1 + z0518 = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + (1 + (1 + z0)) :|: z = 1 + 1, 1 = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + (1 + (1 + z0) + (1 + z0)) :|: z = 1 + (1 + z0414), z0414 >= 0, 1 + z0414 = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + (1 + (1 + z0) + (1 + z0)) :|: z = 1 + 1, 1 = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ---------------------------------------- (57) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (58) Obligation: Complexity RNTS consisting of the following rules: A__ADD(z, z') -{ 1 }-> 1 + MARK(z') :|: z' >= 0, z = 0 A__FIRST(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 A__TERMS(z) -{ 1 }-> 1 + MARK(z) :|: z >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__terms(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__sqr(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__first(mark(z03), mark(z1''))) + MARK(1 + z03 + z1'') :|: z = 1 + (1 + z03 + z1''), z03 >= 0, z1'' >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__dbl(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(a__add(mark(z01), mark(z1'))) + MARK(1 + z01 + z1') :|: z = 1 + (1 + z01 + z1'), z01 >= 0, z1' >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__TERMS(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__TERMS(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(1 + (z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(1 + mark(z04) + z11) + MARK(1 + z04 + z11) :|: z04 >= 0, z = 1 + (1 + z04 + z11), z11 >= 0 MARK(z) -{ 1 }-> 1 + A__FIRST(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__FIRST(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__add(z, z') -{ 0 }-> mark(z') :|: z' >= 0, z = 0 a__add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__add(z, z') -{ 0 }-> 1 + (1 + (z - 1) + z') :|: z' >= 0, z - 1 >= 0 a__add(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__dbl(z) -{ 0 }-> 0 :|: z = 0 a__dbl(z) -{ 0 }-> 0 :|: z >= 0 a__dbl(z) -{ 0 }-> 1 + z :|: z >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + (1 + (z - 1))) :|: z - 1 >= 0 a__first(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0 a__first(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__first(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__first(z, z') -{ 0 }-> 1 + mark(z1) + (1 + (z - 1) + z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 a__sqr(z) -{ 0 }-> 0 :|: z = 0 a__sqr(z) -{ 0 }-> 0 :|: z >= 0 a__sqr(z) -{ 0 }-> 1 + z :|: z >= 0 a__sqr(z) -{ 0 }-> 1 + (1 + (1 + (z - 1)) + (1 + (z - 1))) :|: z - 1 >= 0 a__terms(z) -{ 0 }-> 0 :|: z >= 0 a__terms(z) -{ 0 }-> 1 + z :|: z >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__terms(mark(z - 1)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__sqr(mark(z - 1)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__first(mark(z0395), mark(z1147)))) + (1 + (1 + (1 + z0395 + z1147))) :|: z1147 >= 0, z0395 >= 0, z = 1 + z0395 + z1147 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__dbl(mark(z - 1)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(a__add(mark(z0393), mark(z1146)))) + (1 + (1 + (1 + z0393 + z1146))) :|: z = 1 + z0393 + z1146, z1146 >= 0, z0393 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(1 + mark(z - 1))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(1 + mark(z0396) + z1148)) + (1 + (1 + (1 + z0396 + z1148))) :|: z = 1 + z0396 + z1148, z0396 >= 0, z1148 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + 0) + (1 + (1 + z)) :|: z >= 0, v0 >= 0, 0 = v0 a__terms(z) -{ 0 }-> 1 + (1 + 0) + (1 + (1 + z)) :|: z >= 0, 0 = 0 a__terms(z) -{ 0 }-> 1 + (1 + 0) + (1 + (1 + 1)) :|: z = 1, v0 >= 0, 1 = v0 a__terms(z) -{ 0 }-> 1 + (1 + 0) + (1 + (1 + 0)) :|: z = 0, v0 >= 0, 0 = v0 a__terms(z) -{ 0 }-> 1 + (1 + 0) + (1 + (1 + 0)) :|: z = 0, 0 = 0 a__terms(z) -{ 0 }-> 1 + (1 + 0) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0, v0 >= 0, 1 + (z - 1) = v0 a__terms(z) -{ 0 }-> 1 + (1 + (1 + z0)) + (1 + (1 + 1)) :|: z = 1, 1 = z0, z0 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + (1 + z0)) + (1 + (1 + 0)) :|: z = 0, 0 = z0, z0 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + (1 + z0)) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0, 1 + (z - 1) = z0, z0 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + (1 + z0')) + (1 + (1 + z)) :|: z >= 0, 0 = z0', z0' >= 0 a__terms(z) -{ 0 }-> 1 + (1 + (1 + (1 + (1 + z0) + (1 + z0)))) + (1 + (1 + 1)) :|: z = 1, 1 = 1 + z0, z0 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + (1 + (1 + (1 + z0) + (1 + z0)))) + (1 + (1 + (1 + (z - 1)))) :|: z - 1 >= 0, 1 + (z - 1) = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__terms(a__terms(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__terms(a__sqr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__terms(a__first(mark(z0403), mark(z1150))) :|: z0403 >= 0, z1150 >= 0, z = 1 + (1 + z0403 + z1150) mark(z) -{ 0 }-> a__terms(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__terms(a__add(mark(z0401), mark(z1149))) :|: z = 1 + (1 + z0401 + z1149), z0401 >= 0, z1149 >= 0 mark(z) -{ 0 }-> a__terms(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__terms(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__terms(0) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__terms(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__terms(1 + (z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__terms(1 + mark(z0404) + z1151) :|: z1151 >= 0, z0404 >= 0, z = 1 + (1 + z0404 + z1151) mark(z) -{ 0 }-> a__sqr(a__terms(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__sqr(a__sqr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__sqr(a__first(mark(z0411), mark(z1153))) :|: z = 1 + (1 + z0411 + z1153), z1153 >= 0, z0411 >= 0 mark(z) -{ 0 }-> a__sqr(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__sqr(a__add(mark(z0409), mark(z1152))) :|: z0409 >= 0, z = 1 + (1 + z0409 + z1152), z1152 >= 0 mark(z) -{ 0 }-> a__sqr(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__sqr(1 + mark(z0412) + z1154) :|: z1154 >= 0, z = 1 + (1 + z0412 + z1154), z0412 >= 0 mark(z) -{ 0 }-> a__first(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__dbl(a__terms(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__dbl(a__sqr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__dbl(a__first(mark(z0515), mark(z1192))) :|: z0515 >= 0, z1192 >= 0, z = 1 + (1 + z0515 + z1192) mark(z) -{ 0 }-> a__dbl(a__dbl(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__dbl(a__add(mark(z0513), mark(z1191))) :|: z = 1 + (1 + z0513 + z1191), z1191 >= 0, z0513 >= 0 mark(z) -{ 0 }-> a__dbl(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__dbl(1 + mark(z0516) + z1193) :|: z1193 >= 0, z0516 >= 0, z = 1 + (1 + z0516 + z1193) mark(z) -{ 0 }-> a__add(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 0 :|: z - 2 >= 0, v0 >= 0, 1 + (z - 2) = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z = 1 + 0, 0 = 0 mark(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0 mark(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0 mark(z) -{ 0 }-> 0 :|: z - 1 >= 0, 0 = 0 mark(z) -{ 0 }-> 1 + z0 :|: z - 2 >= 0, 1 + (z - 2) = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 1, 1 = z0, z0 >= 0 mark(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0 mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> 1 + (z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> 1 + (1 + (1 + z0)) :|: z - 2 >= 0, 1 + (z - 2) = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + (1 + (1 + z0)) :|: z = 1 + 1, 1 = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + (1 + (1 + z0) + (1 + z0)) :|: z - 2 >= 0, 1 + (z - 2) = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + (1 + (1 + z0) + (1 + z0)) :|: z = 1 + 1, 1 = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ---------------------------------------- (59) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: a__terms(v0) -> null_a__terms [0] a__sqr(v0) -> null_a__sqr [0] a__dbl(v0) -> null_a__dbl [0] a__add(v0, v1) -> null_a__add [0] a__first(v0, v1) -> null_a__first [0] mark(v0) -> null_mark [0] A__ADD(v0, v1) -> null_A__ADD [0] A__FIRST(v0, v1) -> null_A__FIRST [0] MARK(v0) -> null_MARK [0] And the following fresh constants: null_a__terms, null_a__sqr, null_a__dbl, null_a__add, null_a__first, null_mark, null_A__ADD, null_A__FIRST, null_MARK, const ---------------------------------------- (60) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__ADD(0, z0) -> c8(MARK(z0)) [1] A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) [1] MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) [1] MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) [1] MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) [1] MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) [1] MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c21(MARK(z0)) [1] MARK(recip(z0)) -> c22(MARK(z0)) [1] A__TERMS(z0) -> c(MARK(z0)) [1] MARK(sqr(z0)) -> c15(MARK(z0)) [1] MARK(dbl(z0)) -> c18(MARK(z0)) [1] a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) [0] a__terms(z0) -> terms(z0) [0] a__sqr(0) -> 0 [0] a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) [0] a__sqr(z0) -> sqr(z0) [0] a__dbl(0) -> 0 [0] a__dbl(s(z0)) -> s(s(dbl(z0))) [0] a__dbl(z0) -> dbl(z0) [0] a__add(0, z0) -> mark(z0) [0] a__add(s(z0), z1) -> s(add(z0, z1)) [0] a__add(z0, z1) -> add(z0, z1) [0] a__first(0, z0) -> nil [0] a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) [0] a__first(z0, z1) -> first(z0, z1) [0] mark(terms(z0)) -> a__terms(mark(z0)) [0] mark(sqr(z0)) -> a__sqr(mark(z0)) [0] mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) [0] mark(dbl(z0)) -> a__dbl(mark(z0)) [0] mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(recip(z0)) -> recip(mark(z0)) [0] mark(s(z0)) -> s(z0) [0] mark(0) -> 0 [0] mark(nil) -> nil [0] a__terms(v0) -> null_a__terms [0] a__sqr(v0) -> null_a__sqr [0] a__dbl(v0) -> null_a__dbl [0] a__add(v0, v1) -> null_a__add [0] a__first(v0, v1) -> null_a__first [0] mark(v0) -> null_mark [0] A__ADD(v0, v1) -> null_A__ADD [0] A__FIRST(v0, v1) -> null_A__FIRST [0] MARK(v0) -> null_MARK [0] The TRS has the following type information: A__ADD :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> c8:null_A__ADD 0 :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c8 :: c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK -> c8:null_A__ADD MARK :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK A__FIRST :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> c12:null_A__FIRST s :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark cons :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c12 :: c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK -> c12:null_A__FIRST terms :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c14 :: c -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK A__TERMS :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> c mark :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark add :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c16 :: c8:null_A__ADD -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK c17 :: c8:null_A__ADD -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK first :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c19 :: c12:null_A__FIRST -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK c20 :: c12:null_A__FIRST -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK c21 :: c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK recip :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c22 :: c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK c :: c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK -> c sqr :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c15 :: c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK dbl :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark c18 :: c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK -> c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK a__terms :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark a__sqr :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark a__dbl :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark a__add :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark a__first :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark -> 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark nil :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__terms :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__sqr :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__dbl :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__add :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_a__first :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_mark :: 0:s:cons:terms:add:first:recip:sqr:dbl:nil:null_a__terms:null_a__sqr:null_a__dbl:null_a__add:null_a__first:null_mark null_A__ADD :: c8:null_A__ADD null_A__FIRST :: c12:null_A__FIRST null_MARK :: c14:c16:c17:c19:c20:c21:c22:c15:c18:null_MARK const :: c Rewrite Strategy: INNERMOST ---------------------------------------- (61) 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 nil => 1 null_a__terms => 0 null_a__sqr => 0 null_a__dbl => 0 null_a__add => 0 null_a__first => 0 null_mark => 0 null_A__ADD => 0 null_A__FIRST => 0 null_MARK => 0 const => 0 ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: A__ADD(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__ADD(z, z') -{ 1 }-> 1 + MARK(z0) :|: z0 >= 0, z = 0, z' = z0 A__FIRST(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__FIRST(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__TERMS(z) -{ 1 }-> 1 + MARK(z0) :|: z = z0, z0 >= 0 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__TERMS(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__FIRST(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__FIRST(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ADD(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__add(z, z') -{ 0 }-> mark(z0) :|: z0 >= 0, z = 0, z' = z0 a__add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__add(z, z') -{ 0 }-> 1 + (1 + z0 + z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0 a__add(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__dbl(z) -{ 0 }-> 0 :|: z = 0 a__dbl(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__dbl(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__dbl(z) -{ 0 }-> 1 + (1 + (1 + z0)) :|: z = 1 + z0, z0 >= 0 a__first(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0 a__first(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__first(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__first(z, z') -{ 0 }-> 1 + mark(z1) + (1 + z0 + z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__sqr(z) -{ 0 }-> 0 :|: z = 0 a__sqr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__sqr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__sqr(z) -{ 0 }-> 1 + (1 + (1 + z0) + (1 + z0)) :|: z = 1 + z0, z0 >= 0 a__terms(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__terms(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__terms(z) -{ 0 }-> 1 + (1 + a__sqr(mark(z0))) + (1 + (1 + z0)) :|: z = z0, z0 >= 0 mark(z) -{ 0 }-> a__terms(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__sqr(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__first(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__dbl(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__add(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(z0, z1)) -> c16(A__ADD(mark(z0), mark(z1)), MARK(z0)) by MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c16(A__ADD(s(z0), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)), MARK(0)) MARK(add(nil, x1)) -> c16(A__ADD(nil, mark(x1)), MARK(nil)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c16(A__ADD(s(z0), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)), MARK(0)) MARK(add(nil, x1)) -> c16(A__ADD(nil, mark(x1)), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(s(z0), x1)) -> c16(A__ADD(s(z0), mark(x1)), MARK(s(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)), MARK(0)) MARK(add(nil, x1)) -> c16(A__ADD(nil, mark(x1)), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c17_2, c19_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2 ---------------------------------------- (65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(add(s(z0), x1)) -> c16(A__ADD(s(z0), mark(x1)), MARK(s(z0))) MARK(add(nil, x1)) -> c16(A__ADD(nil, mark(x1)), MARK(nil)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)), MARK(0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(A__ADD(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c17_2, c19_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c17_2, c19_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(z0, z1)) -> c17(A__ADD(mark(z0), mark(z1)), MARK(z1)) by MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)), MARK(s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0), MARK(0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil), MARK(nil)) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(add(recip(z0), x1)) -> c17(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c17(A__ADD(s(z0), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(nil, x1)) -> c17(A__ADD(nil, mark(x1)), MARK(x1)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)), MARK(s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0), MARK(0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil), MARK(nil)) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(add(recip(z0), x1)) -> c17(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c17(A__ADD(s(z0), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(nil, x1)) -> c17(A__ADD(nil, mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0)), MARK(s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0), MARK(0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil), MARK(nil)) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(A__ADD(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(add(recip(z0), x1)) -> c17(A__ADD(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(add(s(z0), x1)) -> c17(A__ADD(s(z0), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(nil, x1)) -> c17(A__ADD(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c19_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c19_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(z0, z1)) -> c19(A__FIRST(mark(z0), mark(z1)), MARK(z0)) by MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c19(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c19(A__FIRST(mark(x0), s(z0)), MARK(x0)) MARK(first(x0, 0)) -> c19(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c19(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c19(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)), MARK(s(z0))) MARK(first(0, x1)) -> c19(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c19(A__FIRST(nil, mark(x1)), MARK(nil)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c19(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c19(A__FIRST(mark(x0), s(z0)), MARK(x0)) MARK(first(x0, 0)) -> c19(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c19(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c19(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)), MARK(s(z0))) MARK(first(0, x1)) -> c19(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c19(A__FIRST(nil, mark(x1)), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c19(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c19(A__FIRST(mark(x0), s(z0)), MARK(x0)) MARK(first(x0, 0)) -> c19(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c19(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c19(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)), MARK(s(z0))) MARK(first(0, x1)) -> c19(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c19(A__FIRST(nil, mark(x1)), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2 ---------------------------------------- (75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(0, x1)) -> c19(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c19(A__FIRST(nil, mark(x1)), MARK(nil)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c19(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c19(A__FIRST(mark(x0), s(z0)), MARK(x0)) MARK(first(x0, 0)) -> c19(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c19(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c19(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, recip(z0))) -> c19(A__FIRST(mark(x0), recip(mark(z0))), MARK(x0)) MARK(first(x0, s(z0))) -> c19(A__FIRST(mark(x0), s(z0)), MARK(x0)) MARK(first(x0, 0)) -> c19(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c19(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c19(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(A__FIRST(recip(mark(z0)), mark(x1)), MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c20_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(z0, z1)) -> c20(A__FIRST(mark(z0), mark(z1)), MARK(z1)) by MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c20(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c20(A__FIRST(mark(x0), s(z0)), MARK(s(z0))) MARK(first(x0, 0)) -> c20(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c20(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c20(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c20(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c20(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c20(A__FIRST(nil, mark(x1)), MARK(x1)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c20(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c20(A__FIRST(mark(x0), s(z0)), MARK(s(z0))) MARK(first(x0, 0)) -> c20(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c20(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c20(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c20(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c20(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c20(A__FIRST(nil, mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c20(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(x0, s(z0))) -> c20(A__FIRST(mark(x0), s(z0)), MARK(s(z0))) MARK(first(x0, 0)) -> c20(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c20(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c20(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c20(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c20(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c20(A__FIRST(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2 ---------------------------------------- (81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(first(x0, 0)) -> c20(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c20(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(x0, s(z0))) -> c20(A__FIRST(mark(x0), s(z0)), MARK(s(z0))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c20(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c20(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c20(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c20(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c20(A__FIRST(nil, mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, recip(z0))) -> c20(A__FIRST(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c20(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(recip(z0), x1)) -> c20(A__FIRST(recip(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c20(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c20(A__FIRST(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, terms(z0))) -> c16(A__ADD(mark(x0), a__terms(mark(z0))), MARK(x0)) by MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0))) MARK(add(s(z0), terms(x1))) -> c16(A__ADD(s(z0), a__terms(mark(x1))), MARK(s(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))), MARK(0)) MARK(add(nil, terms(x1))) -> c16(A__ADD(nil, a__terms(mark(x1))), MARK(nil)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0))) MARK(add(s(z0), terms(x1))) -> c16(A__ADD(s(z0), a__terms(mark(x1))), MARK(s(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))), MARK(0)) MARK(add(nil, terms(x1))) -> c16(A__ADD(nil, a__terms(mark(x1))), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0))) MARK(add(s(z0), terms(x1))) -> c16(A__ADD(s(z0), a__terms(mark(x1))), MARK(s(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))), MARK(0)) MARK(add(nil, terms(x1))) -> c16(A__ADD(nil, a__terms(mark(x1))), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(add(s(z0), terms(x1))) -> c16(A__ADD(s(z0), a__terms(mark(x1))), MARK(s(z0))) MARK(add(nil, terms(x1))) -> c16(A__ADD(nil, a__terms(mark(x1))), MARK(nil)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))), MARK(0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, sqr(z0))) -> c16(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(x0)) by MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0))) MARK(add(s(z0), sqr(x1))) -> c16(A__ADD(s(z0), a__sqr(mark(x1))), MARK(s(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))), MARK(0)) MARK(add(nil, sqr(x1))) -> c16(A__ADD(nil, a__sqr(mark(x1))), MARK(nil)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0))) MARK(add(s(z0), sqr(x1))) -> c16(A__ADD(s(z0), a__sqr(mark(x1))), MARK(s(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))), MARK(0)) MARK(add(nil, sqr(x1))) -> c16(A__ADD(nil, a__sqr(mark(x1))), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0))) MARK(add(s(z0), sqr(x1))) -> c16(A__ADD(s(z0), a__sqr(mark(x1))), MARK(s(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))), MARK(0)) MARK(add(nil, sqr(x1))) -> c16(A__ADD(nil, a__sqr(mark(x1))), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(add(nil, sqr(x1))) -> c16(A__ADD(nil, a__sqr(mark(x1))), MARK(nil)) MARK(add(s(z0), sqr(x1))) -> c16(A__ADD(s(z0), a__sqr(mark(x1))), MARK(s(z0))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))), MARK(0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, add(z0, z1))) -> c16(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) by MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0))) MARK(add(s(z0), add(x1, x2))) -> c16(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0)) MARK(add(nil, add(x1, x2))) -> c16(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0))) MARK(add(s(z0), add(x1, x2))) -> c16(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0)) MARK(add(nil, add(x1, x2))) -> c16(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0))) MARK(add(s(z0), add(x1, x2))) -> c16(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0)) MARK(add(nil, add(x1, x2))) -> c16(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(add(nil, add(x1, x2))) -> c16(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(nil)) MARK(add(s(z0), add(x1, x2))) -> c16(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, dbl(z0))) -> c16(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(x0)) by MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0))) MARK(add(s(z0), dbl(x1))) -> c16(A__ADD(s(z0), a__dbl(mark(x1))), MARK(s(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))), MARK(0)) MARK(add(nil, dbl(x1))) -> c16(A__ADD(nil, a__dbl(mark(x1))), MARK(nil)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0))) MARK(add(s(z0), dbl(x1))) -> c16(A__ADD(s(z0), a__dbl(mark(x1))), MARK(s(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))), MARK(0)) MARK(add(nil, dbl(x1))) -> c16(A__ADD(nil, a__dbl(mark(x1))), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0))) MARK(add(s(z0), dbl(x1))) -> c16(A__ADD(s(z0), a__dbl(mark(x1))), MARK(s(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))), MARK(0)) MARK(add(nil, dbl(x1))) -> c16(A__ADD(nil, a__dbl(mark(x1))), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(add(nil, dbl(x1))) -> c16(A__ADD(nil, a__dbl(mark(x1))), MARK(nil)) MARK(add(s(z0), dbl(x1))) -> c16(A__ADD(s(z0), a__dbl(mark(x1))), MARK(s(z0))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))), MARK(0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, first(z0, z1))) -> c16(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) by MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0))) MARK(add(s(z0), first(x1, x2))) -> c16(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(add(nil, first(x1, x2))) -> c16(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0))) MARK(add(s(z0), first(x1, x2))) -> c16(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(add(nil, first(x1, x2))) -> c16(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0))) MARK(add(s(z0), first(x1, x2))) -> c16(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(add(nil, first(x1, x2))) -> c16(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(add(nil, first(x1, x2))) -> c16(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(nil)) MARK(add(s(z0), first(x1, x2))) -> c16(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, cons(z0, z1))) -> c16(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(x0)) by MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0))) MARK(add(s(z0), cons(x1, x2))) -> c16(A__ADD(s(z0), cons(mark(x1), x2)), MARK(s(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)), MARK(0)) MARK(add(nil, cons(x1, x2))) -> c16(A__ADD(nil, cons(mark(x1), x2)), MARK(nil)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0))) MARK(add(s(z0), cons(x1, x2))) -> c16(A__ADD(s(z0), cons(mark(x1), x2)), MARK(s(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)), MARK(0)) MARK(add(nil, cons(x1, x2))) -> c16(A__ADD(nil, cons(mark(x1), x2)), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0))) MARK(add(s(z0), cons(x1, x2))) -> c16(A__ADD(s(z0), cons(mark(x1), x2)), MARK(s(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)), MARK(0)) MARK(add(nil, cons(x1, x2))) -> c16(A__ADD(nil, cons(mark(x1), x2)), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (117) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(add(s(z0), cons(x1, x2))) -> c16(A__ADD(s(z0), cons(mark(x1), x2)), MARK(s(z0))) MARK(add(nil, cons(x1, x2))) -> c16(A__ADD(nil, cons(mark(x1), x2)), MARK(nil)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)), MARK(0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> 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MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, recip(z0))) -> c16(A__ADD(mark(x0), recip(mark(z0))), MARK(x0)) by MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(z0))) MARK(add(s(z0), recip(x1))) -> c16(A__ADD(s(z0), recip(mark(x1))), MARK(s(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))), MARK(0)) MARK(add(nil, recip(x1))) -> c16(A__ADD(nil, recip(mark(x1))), MARK(nil)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(z0))) MARK(add(s(z0), recip(x1))) -> c16(A__ADD(s(z0), recip(mark(x1))), MARK(s(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))), MARK(0)) MARK(add(nil, recip(x1))) -> c16(A__ADD(nil, recip(mark(x1))), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), 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c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(z0))) MARK(add(s(z0), recip(x1))) -> c16(A__ADD(s(z0), recip(mark(x1))), MARK(s(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))), MARK(0)) MARK(add(nil, recip(x1))) -> c16(A__ADD(nil, recip(mark(x1))), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(add(nil, recip(x1))) -> c16(A__ADD(nil, recip(mark(x1))), MARK(nil)) MARK(add(s(z0), recip(x1))) -> c16(A__ADD(s(z0), recip(mark(x1))), MARK(s(z0))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))), MARK(0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, s(z0))) -> c16(A__ADD(mark(x0), s(z0)), MARK(x0)) by MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(A__ADD(cons(mark(z0), z1), s(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(A__ADD(recip(mark(z0)), s(x1)), MARK(recip(z0))) MARK(add(s(z0), s(x1))) -> c16(A__ADD(s(z0), s(x1)), MARK(s(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)), MARK(0)) MARK(add(nil, s(x1))) -> c16(A__ADD(nil, s(x1)), MARK(nil)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(A__ADD(cons(mark(z0), z1), s(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(A__ADD(recip(mark(z0)), s(x1)), MARK(recip(z0))) MARK(add(s(z0), s(x1))) -> c16(A__ADD(s(z0), s(x1)), MARK(s(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)), MARK(0)) MARK(add(nil, s(x1))) -> c16(A__ADD(nil, s(x1)), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), 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MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(A__ADD(cons(mark(z0), z1), s(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(A__ADD(recip(mark(z0)), s(x1)), MARK(recip(z0))) MARK(add(s(z0), s(x1))) -> c16(A__ADD(s(z0), s(x1)), MARK(s(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)), MARK(0)) MARK(add(nil, s(x1))) -> c16(A__ADD(nil, s(x1)), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(add(s(z0), s(x1))) -> c16(A__ADD(s(z0), s(x1)), MARK(s(z0))) MARK(add(nil, s(x1))) -> c16(A__ADD(nil, s(x1)), MARK(nil)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(A__ADD(cons(mark(z0), z1), s(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(A__ADD(recip(mark(z0)), s(x1)), MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)), MARK(0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, 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c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(A__ADD(cons(mark(z0), z1), s(x1)), MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(A__ADD(recip(mark(z0)), s(x1)), MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), 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c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, 0)) -> c16(A__ADD(mark(x0), 0), MARK(x0)) by MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(A__ADD(cons(mark(z0), z1), 0), MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(A__ADD(recip(mark(z0)), 0), MARK(recip(z0))) MARK(add(s(z0), 0)) -> c16(A__ADD(s(z0), 0), MARK(s(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0), MARK(0)) MARK(add(nil, 0)) -> c16(A__ADD(nil, 0), MARK(nil)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(A__ADD(cons(mark(z0), z1), 0), MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(A__ADD(recip(mark(z0)), 0), MARK(recip(z0))) MARK(add(s(z0), 0)) -> c16(A__ADD(s(z0), 0), MARK(s(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0), MARK(0)) MARK(add(nil, 0)) -> c16(A__ADD(nil, 0), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) 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a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(A__ADD(cons(mark(z0), z1), 0), MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(A__ADD(recip(mark(z0)), 0), MARK(recip(z0))) MARK(add(s(z0), 0)) -> c16(A__ADD(s(z0), 0), MARK(s(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0), MARK(0)) MARK(add(nil, 0)) -> c16(A__ADD(nil, 0), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (135) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(add(s(z0), 0)) -> c16(A__ADD(s(z0), 0), MARK(s(z0))) MARK(add(nil, 0)) -> c16(A__ADD(nil, 0), MARK(nil)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(A__ADD(cons(mark(z0), z1), 0), MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(A__ADD(recip(mark(z0)), 0), MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0), MARK(0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(A__ADD(cons(mark(z0), z1), 0), MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(A__ADD(recip(mark(z0)), 0), MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), 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x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, nil)) -> c16(A__ADD(mark(x0), nil), MARK(x0)) by MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(A__ADD(cons(mark(z0), z1), nil), MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(A__ADD(recip(mark(z0)), nil), MARK(recip(z0))) MARK(add(s(z0), nil)) -> c16(A__ADD(s(z0), nil), MARK(s(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil), MARK(0)) MARK(add(nil, nil)) -> c16(A__ADD(nil, nil), MARK(nil)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, 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MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), 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-> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), 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c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, 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c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(A__ADD(cons(mark(z0), z1), nil), MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(A__ADD(recip(mark(z0)), nil), MARK(recip(z0))) MARK(add(s(z0), nil)) -> c16(A__ADD(s(z0), nil), MARK(s(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil), MARK(0)) MARK(add(nil, nil)) -> c16(A__ADD(nil, nil), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(A__ADD(cons(mark(z0), z1), nil), MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(A__ADD(recip(mark(z0)), nil), MARK(recip(z0))) MARK(add(s(z0), nil)) -> c16(A__ADD(s(z0), nil), MARK(s(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil), MARK(0)) MARK(add(nil, nil)) -> c16(A__ADD(nil, nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (141) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(add(s(z0), nil)) -> c16(A__ADD(s(z0), nil), MARK(s(z0))) MARK(add(nil, nil)) -> c16(A__ADD(nil, nil), MARK(nil)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(A__ADD(cons(mark(z0), z1), nil), MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(A__ADD(recip(mark(z0)), nil), MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil), MARK(0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, 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MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), 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c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 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first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(A__ADD(cons(mark(z0), z1), nil), MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(A__ADD(recip(mark(z0)), nil), MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil), MARK(0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(terms(z0), x1)) -> c16(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) by MARK(add(terms(x0), terms(z0))) -> c16(A__ADD(a__terms(mark(x0)), a__terms(mark(z0))), MARK(terms(x0))) MARK(add(terms(x0), sqr(z0))) -> c16(A__ADD(a__terms(mark(x0)), a__sqr(mark(z0))), MARK(terms(x0))) MARK(add(terms(x0), add(z0, z1))) -> c16(A__ADD(a__terms(mark(x0)), a__add(mark(z0), mark(z1))), MARK(terms(x0))) MARK(add(terms(x0), dbl(z0))) -> c16(A__ADD(a__terms(mark(x0)), a__dbl(mark(z0))), MARK(terms(x0))) MARK(add(terms(x0), first(z0, z1))) -> c16(A__ADD(a__terms(mark(x0)), a__first(mark(z0), mark(z1))), MARK(terms(x0))) MARK(add(terms(x0), cons(z0, z1))) -> c16(A__ADD(a__terms(mark(x0)), cons(mark(z0), z1)), MARK(terms(x0))) MARK(add(terms(x0), recip(z0))) -> c16(A__ADD(a__terms(mark(x0)), recip(mark(z0))), MARK(terms(x0))) MARK(add(terms(x0), s(z0))) -> c16(A__ADD(a__terms(mark(x0)), s(z0)), MARK(terms(x0))) MARK(add(terms(x0), 0)) -> c16(A__ADD(a__terms(mark(x0)), 0), MARK(terms(x0))) MARK(add(terms(x0), nil)) -> c16(A__ADD(a__terms(mark(x0)), nil), MARK(terms(x0))) MARK(add(terms(x0), x1)) -> c16(A__ADD(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))), mark(x1)), MARK(terms(x0))) MARK(add(terms(x0), x1)) -> c16(A__ADD(terms(mark(x0)), mark(x1)), MARK(terms(x0))) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> 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c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(x0), x1)) -> c16(A__ADD(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))), mark(x1)), MARK(terms(x0))) MARK(add(terms(x0), x1)) -> c16(A__ADD(terms(mark(x0)), mark(x1)), MARK(terms(x0))) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(x0), x1)) -> c16(A__ADD(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))), mark(x1)), MARK(terms(x0))) MARK(add(terms(x0), x1)) -> c16(A__ADD(terms(mark(x0)), mark(x1)), MARK(terms(x0))) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(sqr(z0), x1)) -> c16(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) by MARK(add(sqr(x0), terms(z0))) -> c16(A__ADD(a__sqr(mark(x0)), a__terms(mark(z0))), MARK(sqr(x0))) MARK(add(sqr(x0), sqr(z0))) -> c16(A__ADD(a__sqr(mark(x0)), a__sqr(mark(z0))), MARK(sqr(x0))) MARK(add(sqr(x0), add(z0, z1))) -> c16(A__ADD(a__sqr(mark(x0)), a__add(mark(z0), mark(z1))), MARK(sqr(x0))) MARK(add(sqr(x0), dbl(z0))) -> c16(A__ADD(a__sqr(mark(x0)), a__dbl(mark(z0))), MARK(sqr(x0))) MARK(add(sqr(x0), first(z0, z1))) -> c16(A__ADD(a__sqr(mark(x0)), a__first(mark(z0), mark(z1))), MARK(sqr(x0))) MARK(add(sqr(x0), cons(z0, z1))) -> c16(A__ADD(a__sqr(mark(x0)), cons(mark(z0), z1)), MARK(sqr(x0))) MARK(add(sqr(x0), recip(z0))) -> c16(A__ADD(a__sqr(mark(x0)), recip(mark(z0))), MARK(sqr(x0))) MARK(add(sqr(x0), s(z0))) -> c16(A__ADD(a__sqr(mark(x0)), s(z0)), MARK(sqr(x0))) MARK(add(sqr(x0), 0)) -> c16(A__ADD(a__sqr(mark(x0)), 0), MARK(sqr(x0))) MARK(add(sqr(x0), nil)) -> c16(A__ADD(a__sqr(mark(x0)), nil), MARK(sqr(x0))) MARK(add(sqr(x0), x1)) -> c16(A__ADD(sqr(mark(x0)), mark(x1)), MARK(sqr(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) 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MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(x0), x1)) -> c16(A__ADD(sqr(mark(x0)), mark(x1)), MARK(sqr(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(add(z0, z1), x1)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) by MARK(add(add(x0, x1), terms(z0))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), a__terms(mark(z0))), MARK(add(x0, x1))) MARK(add(add(x0, x1), sqr(z0))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), a__sqr(mark(z0))), MARK(add(x0, x1))) MARK(add(add(x0, x1), add(z0, z1))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), a__add(mark(z0), mark(z1))), MARK(add(x0, x1))) MARK(add(add(x0, x1), dbl(z0))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), a__dbl(mark(z0))), MARK(add(x0, x1))) MARK(add(add(x0, x1), first(z0, z1))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(add(x0, x1))) MARK(add(add(x0, x1), cons(z0, z1))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(add(x0, x1))) MARK(add(add(x0, x1), recip(z0))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), recip(mark(z0))), MARK(add(x0, x1))) MARK(add(add(x0, x1), s(z0))) -> c16(A__ADD(a__add(mark(x0), mark(x1)), s(z0)), MARK(add(x0, x1))) MARK(add(add(x0, x1), 0)) -> c16(A__ADD(a__add(mark(x0), mark(x1)), 0), MARK(add(x0, x1))) MARK(add(add(x0, x1), nil)) -> c16(A__ADD(a__add(mark(x0), mark(x1)), nil), MARK(add(x0, x1))) MARK(add(add(x0, x1), x2)) -> c16(A__ADD(add(mark(x0), mark(x1)), mark(x2)), MARK(add(x0, x1))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), 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MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), 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c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), 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recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, x1), x2)) -> c16(A__ADD(add(mark(x0), mark(x1)), mark(x2)), MARK(add(x0, x1))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) 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MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, 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c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(dbl(z0), x1)) -> c16(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) by MARK(add(dbl(x0), terms(z0))) -> c16(A__ADD(a__dbl(mark(x0)), a__terms(mark(z0))), MARK(dbl(x0))) MARK(add(dbl(x0), sqr(z0))) -> c16(A__ADD(a__dbl(mark(x0)), a__sqr(mark(z0))), MARK(dbl(x0))) MARK(add(dbl(x0), add(z0, z1))) -> c16(A__ADD(a__dbl(mark(x0)), a__add(mark(z0), mark(z1))), MARK(dbl(x0))) MARK(add(dbl(x0), dbl(z0))) -> c16(A__ADD(a__dbl(mark(x0)), a__dbl(mark(z0))), MARK(dbl(x0))) MARK(add(dbl(x0), first(z0, z1))) -> c16(A__ADD(a__dbl(mark(x0)), a__first(mark(z0), mark(z1))), MARK(dbl(x0))) MARK(add(dbl(x0), cons(z0, z1))) -> c16(A__ADD(a__dbl(mark(x0)), cons(mark(z0), z1)), MARK(dbl(x0))) MARK(add(dbl(x0), recip(z0))) -> c16(A__ADD(a__dbl(mark(x0)), recip(mark(z0))), MARK(dbl(x0))) MARK(add(dbl(x0), s(z0))) -> c16(A__ADD(a__dbl(mark(x0)), s(z0)), MARK(dbl(x0))) MARK(add(dbl(x0), 0)) -> c16(A__ADD(a__dbl(mark(x0)), 0), MARK(dbl(x0))) MARK(add(dbl(x0), nil)) -> c16(A__ADD(a__dbl(mark(x0)), nil), MARK(dbl(x0))) MARK(add(dbl(x0), x1)) -> c16(A__ADD(dbl(mark(x0)), mark(x1)), MARK(dbl(x0))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), 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MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), 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first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> 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0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), 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MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), 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a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(x0), x1)) -> c16(A__ADD(dbl(mark(x0)), mark(x1)), MARK(dbl(x0))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), 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c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) 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z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_2, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(first(z0, z1), x1)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) by MARK(add(first(x0, x1), terms(z0))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), a__terms(mark(z0))), MARK(first(x0, x1))) MARK(add(first(x0, x1), sqr(z0))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), a__sqr(mark(z0))), MARK(first(x0, x1))) MARK(add(first(x0, x1), add(z0, z1))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), a__add(mark(z0), mark(z1))), MARK(first(x0, x1))) MARK(add(first(x0, x1), dbl(z0))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), a__dbl(mark(z0))), MARK(first(x0, x1))) MARK(add(first(x0, x1), first(z0, z1))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(x0, x1))) MARK(add(first(x0, x1), cons(z0, z1))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(first(x0, x1))) MARK(add(first(x0, x1), recip(z0))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), recip(mark(z0))), MARK(first(x0, x1))) MARK(add(first(x0, x1), s(z0))) -> c16(A__ADD(a__first(mark(x0), mark(x1)), s(z0)), MARK(first(x0, x1))) MARK(add(first(x0, x1), 0)) -> c16(A__ADD(a__first(mark(x0), mark(x1)), 0), MARK(first(x0, x1))) MARK(add(first(x0, x1), nil)) -> c16(A__ADD(a__first(mark(x0), mark(x1)), nil), MARK(first(x0, x1))) MARK(add(first(x0, x1), x2)) -> c16(A__ADD(first(mark(x0), mark(x1)), mark(x2)), MARK(first(x0, x1))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, x1), x2)) -> c16(A__ADD(first(mark(x0), mark(x1)), mark(x2)), MARK(first(x0, x1))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) 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c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> 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recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, x1), x2)) -> c16(A__ADD(first(mark(x0), mark(x1)), mark(x2)), MARK(first(x0, x1))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) 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c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, terms(z0))) -> c17(A__ADD(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) by MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(A__ADD(s(z0), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(A__ADD(nil, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) 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c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), 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MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(A__ADD(s(z0), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(A__ADD(nil, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), 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MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), 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c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(A__ADD(recip(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(A__ADD(s(z0), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(A__ADD(nil, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, 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MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) 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c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> 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MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, 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MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), 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MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, sqr(z0))) -> c17(A__ADD(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) by MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(A__ADD(s(z0), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(A__ADD(nil, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), 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MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), 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MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(A__ADD(s(z0), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(A__ADD(nil, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) 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c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), 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c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), 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c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(A__ADD(recip(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(A__ADD(s(z0), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(A__ADD(nil, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) 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c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), 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MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> 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MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), 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MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) 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c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> 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mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> 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c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, add(z0, z1))) -> c17(A__ADD(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) by MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0)))) MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0)))) MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1)))) MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0)))) MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1)))) MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1)))) MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0)))) MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0)))) MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil))) MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2))) MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2))) MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> 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c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0)))) MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0)))) MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1)))) MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0)))) MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1)))) MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1)))) MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0)))) MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0)))) MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil))) MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2))) MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2))) MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) 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first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0)))) MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0)))) MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1)))) MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0)))) MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1)))) MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1)))) MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0)))) MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0)))) MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil))) MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2))) MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2))) MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(A__ADD(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(A__ADD(s(z0), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(A__ADD(nil, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 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first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0)))) MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0)))) MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1)))) MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0)))) MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1)))) MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1)))) MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0)))) MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0)))) MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil))) MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2))) MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2))) MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> 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c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0)))) MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0)))) MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1)))) MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0)))) MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1)))) MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1)))) MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0)))) MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0)))) MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil))) MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2))) MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2))) MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (177) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, dbl(z0))) -> c17(A__ADD(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) by MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(A__ADD(s(z0), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(A__ADD(nil, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, 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z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(A__ADD(s(z0), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(A__ADD(nil, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) 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c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(A__ADD(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(A__ADD(recip(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(A__ADD(s(z0), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(A__ADD(nil, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) 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MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> 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c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) 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c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), 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c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), 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c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0)))) MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0)))) MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1)))) MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0)))) MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1)))) MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1)))) MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0)))) MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0)))) MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil))) MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2))) MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2))) MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (181) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, first(z0, z1))) -> c17(A__ADD(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) by MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> 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MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), 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MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), 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a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(A__ADD(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(A__ADD(s(z0), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(A__ADD(nil, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) 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MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), 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MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) 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c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1)))) MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0)))) MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0)))) MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil))) MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2))) MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2))) MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, cons(z0, z1))) -> c17(A__ADD(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) by MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(A__ADD(s(z0), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(A__ADD(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) 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c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), 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mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0)))) MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0)))) MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1)))) MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0)))) MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1)))) MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1)))) MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0)))) MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0)))) MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil))) MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2))) MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2))) MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(A__ADD(s(z0), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(A__ADD(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) 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x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, 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c17(A__ADD(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(A__ADD(recip(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(A__ADD(s(z0), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(A__ADD(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), 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a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), 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MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (189) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, recip(z0))) -> c17(A__ADD(mark(x0), recip(mark(z0))), MARK(recip(z0))) by MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(A__ADD(s(z0), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(A__ADD(nil, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), 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c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), 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mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0)))) MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0)))) MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1)))) MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0)))) MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1)))) MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1)))) MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0)))) MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0)))) MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil))) MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2))) MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2))) MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(A__ADD(s(z0), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(A__ADD(nil, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), 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c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(A__ADD(cons(mark(z0), z1), recip(mark(x1))), MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(A__ADD(recip(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(A__ADD(s(z0), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(A__ADD(nil, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) 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c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), 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c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(x0, add(x1, 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c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil))) MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2))) MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2))) MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(terms(z0), x1)) -> c17(A__ADD(a__terms(mark(z0)), mark(x1)), MARK(x1)) by MARK(add(terms(x0), terms(z0))) -> c17(A__ADD(a__terms(mark(x0)), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(terms(x0), sqr(z0))) -> c17(A__ADD(a__terms(mark(x0)), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(terms(x0), add(z0, z1))) -> c17(A__ADD(a__terms(mark(x0)), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(terms(x0), dbl(z0))) -> c17(A__ADD(a__terms(mark(x0)), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(terms(x0), first(z0, z1))) -> c17(A__ADD(a__terms(mark(x0)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(terms(x0), cons(z0, z1))) -> c17(A__ADD(a__terms(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(terms(x0), recip(z0))) -> c17(A__ADD(a__terms(mark(x0)), recip(mark(z0))), MARK(recip(z0))) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)), MARK(s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0), MARK(0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil), MARK(nil)) MARK(add(terms(x0), x1)) -> c17(A__ADD(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))), mark(x1)), MARK(x1)) MARK(add(terms(x0), x1)) -> c17(A__ADD(terms(mark(x0)), mark(x1)), MARK(x1)) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) 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x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)), MARK(s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0), MARK(0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil), MARK(nil)) MARK(add(terms(x0), x1)) -> c17(A__ADD(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))), mark(x1)), MARK(x1)) MARK(add(terms(x0), x1)) -> c17(A__ADD(terms(mark(x0)), mark(x1)), MARK(x1)) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> 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c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0)), MARK(s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0), MARK(0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil), MARK(nil)) MARK(add(terms(x0), x1)) -> c17(A__ADD(cons(recip(a__sqr(mark(mark(x0)))), terms(s(mark(x0)))), mark(x1)), MARK(x1)) MARK(add(terms(x0), x1)) -> c17(A__ADD(terms(mark(x0)), mark(x1)), MARK(x1)) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) 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MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> 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c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), 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c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(sqr(z0), x1)) -> c17(A__ADD(a__sqr(mark(z0)), mark(x1)), MARK(x1)) by MARK(add(sqr(x0), terms(z0))) -> c17(A__ADD(a__sqr(mark(x0)), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(sqr(x0), sqr(z0))) -> c17(A__ADD(a__sqr(mark(x0)), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(sqr(x0), add(z0, z1))) -> c17(A__ADD(a__sqr(mark(x0)), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(sqr(x0), dbl(z0))) -> c17(A__ADD(a__sqr(mark(x0)), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(sqr(x0), first(z0, z1))) -> c17(A__ADD(a__sqr(mark(x0)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(sqr(x0), cons(z0, z1))) -> c17(A__ADD(a__sqr(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(sqr(x0), recip(z0))) -> c17(A__ADD(a__sqr(mark(x0)), recip(mark(z0))), MARK(recip(z0))) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)), MARK(s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0), MARK(0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil), MARK(nil)) MARK(add(sqr(x0), x1)) -> c17(A__ADD(sqr(mark(x0)), mark(x1)), MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), 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recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, 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MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)), MARK(s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0), MARK(0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil), MARK(nil)) MARK(add(sqr(x0), x1)) -> c17(A__ADD(sqr(mark(x0)), mark(x1)), MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), 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a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0)), MARK(s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0), MARK(0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil), MARK(nil)) MARK(add(sqr(x0), x1)) -> c17(A__ADD(sqr(mark(x0)), mark(x1)), MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) 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c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), 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mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, 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MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), 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mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> 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c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), 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-> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(add(z0, z1), x1)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by MARK(add(add(x0, x1), terms(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(add(x0, x1), sqr(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(add(x0, x1), add(z0, z1))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(add(x0, x1), dbl(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(add(x0, x1), first(z0, z1))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(add(x0, x1), cons(z0, z1))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(add(x0, x1), recip(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), recip(mark(z0))), MARK(recip(z0))) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)), MARK(s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0), MARK(0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil), MARK(nil)) MARK(add(add(x0, x1), x2)) -> c17(A__ADD(add(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> 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c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), 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dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 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c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> 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mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)), MARK(s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0), MARK(0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil), MARK(nil)) MARK(add(add(x0, x1), x2)) -> c17(A__ADD(add(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, 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dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0)), MARK(s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0), MARK(0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil), MARK(nil)) MARK(add(add(x0, x1), x2)) -> c17(A__ADD(add(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (203) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), 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x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), 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mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (205) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(dbl(z0), x1)) -> c17(A__ADD(a__dbl(mark(z0)), mark(x1)), MARK(x1)) by MARK(add(dbl(x0), terms(z0))) -> c17(A__ADD(a__dbl(mark(x0)), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(dbl(x0), sqr(z0))) -> c17(A__ADD(a__dbl(mark(x0)), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(dbl(x0), add(z0, z1))) -> c17(A__ADD(a__dbl(mark(x0)), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(dbl(x0), dbl(z0))) -> c17(A__ADD(a__dbl(mark(x0)), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(dbl(x0), first(z0, z1))) -> c17(A__ADD(a__dbl(mark(x0)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(dbl(x0), cons(z0, z1))) -> c17(A__ADD(a__dbl(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(dbl(x0), recip(z0))) -> c17(A__ADD(a__dbl(mark(x0)), recip(mark(z0))), MARK(recip(z0))) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)), MARK(s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0), MARK(0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil), MARK(nil)) MARK(add(dbl(x0), x1)) -> c17(A__ADD(dbl(mark(x0)), mark(x1)), MARK(x1)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), 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a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)), MARK(s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0), MARK(0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil), MARK(nil)) MARK(add(dbl(x0), x1)) -> c17(A__ADD(dbl(mark(x0)), mark(x1)), MARK(x1)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 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MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, 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a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0)), MARK(s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0), MARK(0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil), MARK(nil)) MARK(add(dbl(x0), x1)) -> c17(A__ADD(dbl(mark(x0)), mark(x1)), MARK(x1)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), 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MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) 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c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (209) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(first(z0, z1), x1)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by MARK(add(first(x0, x1), terms(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), a__terms(mark(z0))), MARK(terms(z0))) MARK(add(first(x0, x1), sqr(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(add(first(x0, x1), add(z0, z1))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(add(first(x0, x1), dbl(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(add(first(x0, x1), first(z0, z1))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(add(first(x0, x1), cons(z0, z1))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(add(first(x0, x1), recip(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), recip(mark(z0))), MARK(recip(z0))) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)), MARK(s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0), MARK(0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil), MARK(nil)) MARK(add(first(x0, x1), x2)) -> c17(A__ADD(first(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, 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MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 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first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> 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MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)), MARK(s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0), MARK(0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil), MARK(nil)) MARK(add(first(x0, x1), x2)) -> c17(A__ADD(first(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) 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x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0)), MARK(s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0), MARK(0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil), MARK(nil)) MARK(add(first(x0, x1), x2)) -> c17(A__ADD(first(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, 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MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), 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MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (213) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, s(z0))) -> c17(A__ADD(mark(x0), s(z0))) by MARK(add(terms(z0), s(x1))) -> c17(A__ADD(a__terms(mark(z0)), s(x1))) MARK(add(sqr(z0), s(x1))) -> c17(A__ADD(a__sqr(mark(z0)), s(x1))) MARK(add(add(z0, z1), s(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), s(x1))) MARK(add(dbl(z0), s(x1))) -> c17(A__ADD(a__dbl(mark(z0)), s(x1))) MARK(add(first(z0, z1), s(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), s(x1))) MARK(add(cons(z0, z1), s(x1))) -> c17(A__ADD(cons(mark(z0), z1), s(x1))) MARK(add(recip(z0), s(x1))) -> c17(A__ADD(recip(mark(z0)), s(x1))) MARK(add(s(z0), s(x1))) -> c17(A__ADD(s(z0), s(x1))) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(nil, s(x1))) -> c17(A__ADD(nil, s(x1))) ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> 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MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(cons(z0, z1), s(x1))) -> c17(A__ADD(cons(mark(z0), z1), s(x1))) MARK(add(recip(z0), s(x1))) -> c17(A__ADD(recip(mark(z0)), s(x1))) MARK(add(s(z0), s(x1))) -> c17(A__ADD(s(z0), s(x1))) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(nil, s(x1))) -> c17(A__ADD(nil, s(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), 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x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(cons(z0, z1), s(x1))) -> c17(A__ADD(cons(mark(z0), z1), s(x1))) MARK(add(recip(z0), s(x1))) -> c17(A__ADD(recip(mark(z0)), s(x1))) MARK(add(s(z0), s(x1))) -> c17(A__ADD(s(z0), s(x1))) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(nil, s(x1))) -> c17(A__ADD(nil, s(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (215) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: MARK(add(recip(z0), s(x1))) -> c17(A__ADD(recip(mark(z0)), s(x1))) MARK(add(s(z0), s(x1))) -> c17(A__ADD(s(z0), s(x1))) MARK(add(cons(z0, z1), s(x1))) -> c17(A__ADD(cons(mark(z0), z1), s(x1))) MARK(add(nil, s(x1))) -> c17(A__ADD(nil, s(x1))) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> 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MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), 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cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), 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recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> 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mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, 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MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (217) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, 0)) -> c17(A__ADD(mark(x0), 0)) by MARK(add(terms(z0), 0)) -> c17(A__ADD(a__terms(mark(z0)), 0)) MARK(add(sqr(z0), 0)) -> c17(A__ADD(a__sqr(mark(z0)), 0)) MARK(add(add(z0, z1), 0)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), 0)) MARK(add(dbl(z0), 0)) -> c17(A__ADD(a__dbl(mark(z0)), 0)) MARK(add(first(z0, z1), 0)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), 0)) MARK(add(cons(z0, z1), 0)) -> c17(A__ADD(cons(mark(z0), z1), 0)) MARK(add(recip(z0), 0)) -> c17(A__ADD(recip(mark(z0)), 0)) MARK(add(s(z0), 0)) -> c17(A__ADD(s(z0), 0)) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(nil, 0)) -> c17(A__ADD(nil, 0)) ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) 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c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), 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c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), 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MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(cons(z0, z1), 0)) -> c17(A__ADD(cons(mark(z0), z1), 0)) MARK(add(recip(z0), 0)) -> c17(A__ADD(recip(mark(z0)), 0)) MARK(add(s(z0), 0)) -> c17(A__ADD(s(z0), 0)) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(nil, 0)) -> c17(A__ADD(nil, 0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), 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MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) 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c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(cons(z0, z1), 0)) -> c17(A__ADD(cons(mark(z0), z1), 0)) MARK(add(recip(z0), 0)) -> c17(A__ADD(recip(mark(z0)), 0)) MARK(add(s(z0), 0)) -> c17(A__ADD(s(z0), 0)) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(nil, 0)) -> c17(A__ADD(nil, 0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (219) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: MARK(add(recip(z0), 0)) -> c17(A__ADD(recip(mark(z0)), 0)) MARK(add(s(z0), 0)) -> c17(A__ADD(s(z0), 0)) MARK(add(nil, 0)) -> c17(A__ADD(nil, 0)) MARK(add(cons(z0, z1), 0)) -> c17(A__ADD(cons(mark(z0), z1), 0)) ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, 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cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> 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c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) 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c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), 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mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, 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MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), 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mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> 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c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (221) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(add(x0, nil)) -> c17(A__ADD(mark(x0), nil)) by MARK(add(terms(z0), nil)) -> c17(A__ADD(a__terms(mark(z0)), nil)) MARK(add(sqr(z0), nil)) -> c17(A__ADD(a__sqr(mark(z0)), nil)) MARK(add(add(z0, z1), nil)) -> c17(A__ADD(a__add(mark(z0), mark(z1)), nil)) MARK(add(dbl(z0), nil)) -> c17(A__ADD(a__dbl(mark(z0)), nil)) MARK(add(first(z0, z1), nil)) -> c17(A__ADD(a__first(mark(z0), mark(z1)), nil)) MARK(add(cons(z0, z1), nil)) -> c17(A__ADD(cons(mark(z0), z1), nil)) MARK(add(recip(z0), nil)) -> c17(A__ADD(recip(mark(z0)), nil)) MARK(add(s(z0), nil)) -> c17(A__ADD(s(z0), nil)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(add(nil, nil)) -> c17(A__ADD(nil, nil)) ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) 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mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(cons(z0, z1), nil)) -> c17(A__ADD(cons(mark(z0), z1), nil)) MARK(add(recip(z0), nil)) -> c17(A__ADD(recip(mark(z0)), nil)) MARK(add(s(z0), nil)) -> c17(A__ADD(s(z0), nil)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(add(nil, nil)) -> c17(A__ADD(nil, nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 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MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(cons(z0, z1), nil)) -> c17(A__ADD(cons(mark(z0), z1), nil)) MARK(add(recip(z0), nil)) -> c17(A__ADD(recip(mark(z0)), nil)) MARK(add(s(z0), nil)) -> c17(A__ADD(s(z0), nil)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(add(nil, nil)) -> c17(A__ADD(nil, nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (223) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: MARK(add(recip(z0), nil)) -> c17(A__ADD(recip(mark(z0)), nil)) MARK(add(cons(z0, z1), nil)) -> c17(A__ADD(cons(mark(z0), z1), nil)) MARK(add(s(z0), nil)) -> c17(A__ADD(s(z0), nil)) MARK(add(nil, nil)) -> c17(A__ADD(nil, nil)) ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, 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a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), 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c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, 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cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) 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c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 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MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), 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MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, terms(z0))) -> c19(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(x0)) by MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), terms(mark(x1))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), terms(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(A__FIRST(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))), MARK(s(z0))) MARK(first(0, terms(x1))) -> c19(A__FIRST(0, a__terms(mark(x1))), MARK(0)) MARK(first(nil, terms(x1))) -> c19(A__FIRST(nil, a__terms(mark(x1))), MARK(nil)) ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), 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c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), terms(mark(x1))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), terms(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(A__FIRST(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))), MARK(s(z0))) MARK(first(0, terms(x1))) -> c19(A__FIRST(0, a__terms(mark(x1))), MARK(0)) MARK(first(nil, terms(x1))) -> c19(A__FIRST(nil, a__terms(mark(x1))), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) 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MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), terms(mark(x1))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), terms(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(A__FIRST(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))), MARK(s(z0))) MARK(first(0, terms(x1))) -> c19(A__FIRST(0, a__terms(mark(x1))), MARK(0)) MARK(first(nil, terms(x1))) -> c19(A__FIRST(nil, a__terms(mark(x1))), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (227) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(nil, terms(x1))) -> c19(A__FIRST(nil, a__terms(mark(x1))), MARK(nil)) MARK(first(0, terms(x1))) -> c19(A__FIRST(0, a__terms(mark(x1))), MARK(0)) ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> 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MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), 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MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), terms(mark(x1))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), terms(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(A__FIRST(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), 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MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), terms(mark(x1))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), terms(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__terms(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(A__FIRST(recip(mark(z0)), a__terms(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> 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MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, 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a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (231) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, sqr(z0))) -> c19(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(x0)) by MARK(first(x0, sqr(x1))) -> c19(A__FIRST(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), sqr(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(A__FIRST(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))), MARK(s(z0))) MARK(first(0, sqr(x1))) -> c19(A__FIRST(0, a__sqr(mark(x1))), MARK(0)) MARK(first(nil, sqr(x1))) -> c19(A__FIRST(nil, a__sqr(mark(x1))), MARK(nil)) ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, 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z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(x1))) -> c19(A__FIRST(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), sqr(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(A__FIRST(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))), MARK(s(z0))) MARK(first(0, sqr(x1))) -> c19(A__FIRST(0, a__sqr(mark(x1))), MARK(0)) MARK(first(nil, sqr(x1))) -> c19(A__FIRST(nil, a__sqr(mark(x1))), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> 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c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(x1))) -> c19(A__FIRST(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), sqr(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(A__FIRST(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))), MARK(s(z0))) MARK(first(0, sqr(x1))) -> c19(A__FIRST(0, a__sqr(mark(x1))), MARK(0)) MARK(first(nil, sqr(x1))) -> c19(A__FIRST(nil, a__sqr(mark(x1))), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (233) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(nil, sqr(x1))) -> c19(A__FIRST(nil, a__sqr(mark(x1))), MARK(nil)) MARK(first(0, sqr(x1))) -> c19(A__FIRST(0, a__sqr(mark(x1))), MARK(0)) ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> 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recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(x1))) -> c19(A__FIRST(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), sqr(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(A__FIRST(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), 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a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(x1))) -> c19(A__FIRST(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), sqr(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__sqr(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(A__FIRST(recip(mark(z0)), a__sqr(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (235) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> c17(A__ADD(mark(x0), a__terms(nil)), MARK(terms(nil))) MARK(add(terms(z0), terms(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(sqr(z0), terms(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(add(z0, z1), terms(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(dbl(z0), terms(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(first(z0, z1), terms(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(terms(x1))) MARK(add(0, terms(x1))) -> c17(A__ADD(0, a__terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(cons(z0, z1), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(recip(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(s(z0), terms(x1))) -> c17(MARK(terms(x1))) MARK(add(nil, terms(x1))) -> c17(MARK(terms(x1))) MARK(add(x0, sqr(x1))) -> c17(A__ADD(mark(x0), sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(terms(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(sqr(terms(z0)))) MARK(add(x0, sqr(sqr(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(sqr(sqr(z0)))) MARK(add(x0, sqr(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(sqr(add(z0, z1)))) MARK(add(x0, sqr(dbl(z0)))) -> c17(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(sqr(dbl(z0)))) MARK(add(x0, sqr(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(sqr(first(z0, z1)))) MARK(add(x0, sqr(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(sqr(cons(z0, z1)))) MARK(add(x0, sqr(recip(z0)))) -> c17(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(sqr(recip(z0)))) MARK(add(x0, sqr(s(z0)))) -> c17(A__ADD(mark(x0), a__sqr(s(z0))), MARK(sqr(s(z0)))) MARK(add(x0, sqr(0))) -> c17(A__ADD(mark(x0), a__sqr(0)), MARK(sqr(0))) MARK(add(x0, sqr(nil))) -> c17(A__ADD(mark(x0), a__sqr(nil)), MARK(sqr(nil))) MARK(add(terms(z0), sqr(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(sqr(z0), sqr(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(add(z0, z1), sqr(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(dbl(z0), sqr(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(first(z0, z1), sqr(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(0, sqr(x1))) -> c17(A__ADD(0, a__sqr(mark(x1))), MARK(sqr(x1))) MARK(add(x0, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(cons(z0, z1), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(recip(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(s(z0), sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(nil, sqr(x1))) -> c17(MARK(sqr(x1))) MARK(add(x0, add(x1, x2))) -> c17(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(x0, add(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(add(x1, terms(z0)))) MARK(add(x0, add(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(add(x1, sqr(z0)))) MARK(add(x0, add(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(add(x1, add(z0, z1)))) MARK(add(x0, add(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(add(x1, dbl(z0)))) MARK(add(x0, add(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1)))) MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1)))) MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0)))) MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0)))) MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil))) MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2))) MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2))) MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, 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a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) 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nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (237) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, add(z0, z1))) -> c19(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(x0)) by MARK(first(x0, add(x1, x2))) -> c19(A__FIRST(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(0, add(x1, x2))) -> c19(A__FIRST(0, a__add(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, add(x1, x2))) -> c19(A__FIRST(nil, a__add(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (238) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), 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c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 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first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) 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c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, x2))) -> c19(A__FIRST(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(0, add(x1, x2))) -> c19(A__FIRST(0, a__add(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, add(x1, x2))) -> c19(A__FIRST(nil, a__add(mark(x1), mark(x2))), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), 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MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, x2))) -> c19(A__FIRST(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(0, add(x1, x2))) -> c19(A__FIRST(0, a__add(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, add(x1, x2))) -> c19(A__FIRST(nil, a__add(mark(x1), mark(x2))), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (239) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(0, add(x1, x2))) -> c19(A__FIRST(0, a__add(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, add(x1, x2))) -> c19(A__FIRST(nil, a__add(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (240) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) 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z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, x2))) -> c19(A__FIRST(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) 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c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, x2))) -> c19(A__FIRST(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__add(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__add(mark(x1), mark(x2))), MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (241) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (242) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), 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MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), 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c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> c16(MARK(dbl(x0))) MARK(add(first(x0, terms(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(first(x0, terms(z0)))) MARK(add(first(x0, sqr(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(first(x0, sqr(z0)))) MARK(add(first(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, add(z0, z1)))) MARK(add(first(x0, dbl(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(first(x0, dbl(z0)))) MARK(add(first(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(add(first(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(add(first(x0, recip(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(first(x0, recip(z0)))) MARK(add(first(x0, s(z0)), x2)) -> c16(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(first(x0, s(z0)))) MARK(add(first(x0, 0), x2)) -> c16(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(add(first(x0, nil), x2)) -> c16(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(add(first(terms(z0), x1), x2)) -> c16(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(first(terms(z0), x1))) MARK(add(first(sqr(z0), x1), x2)) -> c16(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(first(sqr(z0), x1))) MARK(add(first(add(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(add(z0, z1), x1))) MARK(add(first(dbl(z0), x1), x2)) -> c16(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(first(dbl(z0), x1))) MARK(add(first(first(z0, z1), x1), x2)) -> c16(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(add(first(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(add(first(recip(z0), x1), x2)) -> c16(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(first(recip(z0), x1))) MARK(add(first(s(z0), x1), x2)) -> c16(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(add(first(0, x1), x2)) -> c16(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(add(first(nil, x1), x2)) -> c16(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(add(first(x0, x1), x2)) -> c16(MARK(first(x0, x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(terms(x1))) MARK(add(x0, terms(x1))) -> c17(A__ADD(mark(x0), terms(mark(x1))), MARK(terms(x1))) MARK(add(x0, terms(terms(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(terms(terms(z0)))) MARK(add(x0, terms(sqr(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(terms(sqr(z0)))) MARK(add(x0, terms(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(terms(add(z0, z1)))) MARK(add(x0, terms(dbl(z0)))) -> c17(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(terms(dbl(z0)))) MARK(add(x0, terms(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(terms(first(z0, z1)))) MARK(add(x0, terms(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(terms(cons(z0, z1)))) MARK(add(x0, terms(recip(z0)))) -> c17(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(terms(recip(z0)))) MARK(add(x0, terms(s(z0)))) -> c17(A__ADD(mark(x0), a__terms(s(z0))), MARK(terms(s(z0)))) MARK(add(x0, terms(0))) -> c17(A__ADD(mark(x0), a__terms(0)), MARK(terms(0))) MARK(add(x0, terms(nil))) -> 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c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, 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MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(add(z0, z1), add(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(dbl(z0), add(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(first(z0, z1), add(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(0, add(x1, x2))) -> c17(A__ADD(0, a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(cons(z0, z1), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(recip(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(s(z0), add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(nil, add(x1, x2))) -> c17(MARK(add(x1, x2))) MARK(add(x0, dbl(x1))) -> c17(A__ADD(mark(x0), dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(terms(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(dbl(terms(z0)))) MARK(add(x0, dbl(sqr(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, 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mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), 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c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (243) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, dbl(z0))) -> c19(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(x0)) by MARK(first(x0, dbl(x1))) -> c19(A__FIRST(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0)) MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0)) MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), dbl(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), dbl(x1))) -> c19(A__FIRST(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))), MARK(s(z0))) MARK(first(0, dbl(x1))) -> c19(A__FIRST(0, a__dbl(mark(x1))), MARK(0)) MARK(first(nil, dbl(x1))) -> c19(A__FIRST(nil, a__dbl(mark(x1))), MARK(nil)) ---------------------------------------- (244) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> 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c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) MARK(first(x0, dbl(x1))) -> c19(A__FIRST(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0)) MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0)) MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), dbl(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), dbl(x1))) -> c19(A__FIRST(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))), MARK(s(z0))) MARK(first(0, dbl(x1))) -> c19(A__FIRST(0, a__dbl(mark(x1))), MARK(0)) MARK(first(nil, dbl(x1))) -> c19(A__FIRST(nil, a__dbl(mark(x1))), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), 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a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) MARK(first(x0, dbl(x1))) -> c19(A__FIRST(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0)) MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0)) MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), dbl(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), dbl(x1))) -> c19(A__FIRST(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))), MARK(s(z0))) MARK(first(0, dbl(x1))) -> c19(A__FIRST(0, a__dbl(mark(x1))), MARK(0)) MARK(first(nil, dbl(x1))) -> c19(A__FIRST(nil, a__dbl(mark(x1))), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (245) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(0, dbl(x1))) -> c19(A__FIRST(0, a__dbl(mark(x1))), MARK(0)) MARK(first(nil, dbl(x1))) -> c19(A__FIRST(nil, a__dbl(mark(x1))), MARK(nil)) ---------------------------------------- (246) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) 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c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) MARK(first(x0, dbl(x1))) -> c19(A__FIRST(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0)) MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0)) MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), dbl(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), dbl(x1))) -> c19(A__FIRST(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 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c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) MARK(first(x0, dbl(x1))) -> c19(A__FIRST(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0)) MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0)) MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), dbl(x1))) -> c19(A__FIRST(cons(mark(z0), z1), a__dbl(mark(x1))), MARK(cons(z0, z1))) MARK(first(recip(z0), dbl(x1))) -> c19(A__FIRST(recip(mark(z0)), a__dbl(mark(x1))), MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (247) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (248) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) 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a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, 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cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), 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c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), 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MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) 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c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0)) MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0)) MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, dbl(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1)))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), 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MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), 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a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), 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a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0)) MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0)) MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, dbl(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (249) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, first(z0, z1))) -> c19(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) by MARK(first(x0, first(x1, x2))) -> c19(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), first(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(recip(z0), first(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0))) MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(0, first(x1, x2))) -> c19(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, first(x1, x2))) -> c19(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (250) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), 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a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0)) MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0)) MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, dbl(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1)))) MARK(first(x0, first(x1, x2))) -> c19(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), first(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(recip(z0), first(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0))) MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(0, first(x1, x2))) -> c19(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, first(x1, x2))) -> c19(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil)) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, first(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, first(x1, 0))) -> c16(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(add(x0, first(x1, nil))) -> c16(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(add(x0, first(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, first(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, first(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, first(s(z0), x2))) -> c16(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, first(0, x2))) -> c16(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(add(x0, first(nil, x2))) -> c16(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), first(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), first(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), first(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), first(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), first(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), first(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), first(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, first(x1, x2))) -> c16(A__ADD(0, a__first(mark(x1), mark(x2)))) MARK(add(x0, cons(terms(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(sqr(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(dbl(z0), x2))) -> c16(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(add(x0, cons(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(add(x0, cons(recip(z0), x2))) -> c16(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(x0)) MARK(add(x0, cons(s(z0), x2))) -> c16(A__ADD(mark(x0), cons(s(z0), x2)), MARK(x0)) MARK(add(x0, cons(0, x2))) -> c16(A__ADD(mark(x0), cons(0, x2)), MARK(x0)) MARK(add(x0, cons(nil, x2))) -> c16(A__ADD(mark(x0), cons(nil, x2)), MARK(x0)) MARK(add(terms(z0), cons(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(terms(z0))) MARK(add(sqr(z0), cons(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(sqr(z0))) MARK(add(add(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(add(z0, z1))) MARK(add(dbl(z0), cons(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(dbl(z0))) MARK(add(first(z0, z1), cons(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), cons(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, cons(x1, x2))) -> c16(A__ADD(0, cons(mark(x1), x2))) MARK(add(x0, recip(terms(z0)))) -> c16(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, recip(sqr(z0)))) -> c16(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, recip(add(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(dbl(z0)))) -> c16(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, recip(first(z0, z1)))) -> c16(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, recip(cons(z0, z1)))) -> c16(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, recip(recip(z0)))) -> c16(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(x0)) MARK(add(x0, recip(s(z0)))) -> c16(A__ADD(mark(x0), recip(s(z0))), MARK(x0)) MARK(add(x0, recip(0))) -> c16(A__ADD(mark(x0), recip(0)), MARK(x0)) MARK(add(x0, recip(nil))) -> c16(A__ADD(mark(x0), recip(nil)), MARK(x0)) MARK(add(terms(z0), recip(x1))) -> c16(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), recip(x1))) -> c16(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), recip(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), recip(x1))) -> c16(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), recip(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), recip(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), recip(x1))) -> c16(MARK(recip(z0))) MARK(add(0, recip(x1))) -> c16(A__ADD(0, recip(mark(x1)))) MARK(add(terms(z0), s(x1))) -> c16(A__ADD(a__terms(mark(z0)), s(x1)), MARK(terms(z0))) MARK(add(sqr(z0), s(x1))) -> c16(A__ADD(a__sqr(mark(z0)), s(x1)), MARK(sqr(z0))) MARK(add(add(z0, z1), s(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), s(x1)), MARK(add(z0, z1))) MARK(add(dbl(z0), s(x1))) -> c16(A__ADD(a__dbl(mark(z0)), s(x1)), MARK(dbl(z0))) MARK(add(first(z0, z1), s(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), s(x1)), MARK(first(z0, z1))) MARK(add(cons(z0, z1), s(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), s(x1))) -> c16(MARK(recip(z0))) MARK(add(0, s(x1))) -> c16(A__ADD(0, s(x1))) MARK(add(terms(z0), 0)) -> c16(A__ADD(a__terms(mark(z0)), 0), MARK(terms(z0))) MARK(add(sqr(z0), 0)) -> c16(A__ADD(a__sqr(mark(z0)), 0), MARK(sqr(z0))) MARK(add(add(z0, z1), 0)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), 0), MARK(add(z0, z1))) MARK(add(dbl(z0), 0)) -> c16(A__ADD(a__dbl(mark(z0)), 0), MARK(dbl(z0))) MARK(add(first(z0, z1), 0)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), 0), MARK(first(z0, z1))) MARK(add(cons(z0, z1), 0)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), 0)) -> c16(MARK(recip(z0))) MARK(add(0, 0)) -> c16(A__ADD(0, 0)) MARK(add(terms(z0), nil)) -> c16(A__ADD(a__terms(mark(z0)), nil), MARK(terms(z0))) MARK(add(sqr(z0), nil)) -> c16(A__ADD(a__sqr(mark(z0)), nil), MARK(sqr(z0))) MARK(add(add(z0, z1), nil)) -> c16(A__ADD(a__add(mark(z0), mark(z1)), nil), MARK(add(z0, z1))) MARK(add(dbl(z0), nil)) -> c16(A__ADD(a__dbl(mark(z0)), nil), MARK(dbl(z0))) MARK(add(first(z0, z1), nil)) -> c16(A__ADD(a__first(mark(z0), mark(z1)), nil), MARK(first(z0, z1))) MARK(add(cons(z0, z1), nil)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), nil)) -> c16(MARK(recip(z0))) MARK(add(0, nil)) -> c16(A__ADD(0, nil)) MARK(add(terms(terms(z0)), x1)) -> c16(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(terms(terms(z0)))) MARK(add(terms(sqr(z0)), x1)) -> c16(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(terms(sqr(z0)))) MARK(add(terms(add(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(terms(add(z0, z1)))) MARK(add(terms(dbl(z0)), x1)) -> c16(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(terms(dbl(z0)))) MARK(add(terms(first(z0, z1)), x1)) -> c16(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(terms(first(z0, z1)))) MARK(add(terms(cons(z0, z1)), x1)) -> c16(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(terms(cons(z0, z1)))) MARK(add(terms(recip(z0)), x1)) -> c16(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(terms(recip(z0)))) MARK(add(terms(s(z0)), x1)) -> c16(A__ADD(a__terms(s(z0)), mark(x1)), MARK(terms(s(z0)))) MARK(add(terms(0), x1)) -> c16(A__ADD(a__terms(0), mark(x1)), MARK(terms(0))) MARK(add(terms(nil), x1)) -> c16(A__ADD(a__terms(nil), mark(x1)), MARK(terms(nil))) MARK(add(terms(x0), x1)) -> c16(MARK(terms(x0))) MARK(add(sqr(terms(z0)), x1)) -> c16(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(sqr(terms(z0)))) MARK(add(sqr(sqr(z0)), x1)) -> c16(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(sqr(sqr(z0)))) MARK(add(sqr(add(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(sqr(add(z0, z1)))) MARK(add(sqr(dbl(z0)), x1)) -> c16(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(sqr(dbl(z0)))) MARK(add(sqr(first(z0, z1)), x1)) -> c16(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(sqr(first(z0, z1)))) MARK(add(sqr(cons(z0, z1)), x1)) -> c16(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(sqr(cons(z0, z1)))) MARK(add(sqr(recip(z0)), x1)) -> c16(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(sqr(recip(z0)))) MARK(add(sqr(s(z0)), x1)) -> c16(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(sqr(s(z0)))) MARK(add(sqr(0), x1)) -> c16(A__ADD(a__sqr(0), mark(x1)), MARK(sqr(0))) MARK(add(sqr(nil), x1)) -> c16(A__ADD(a__sqr(nil), mark(x1)), MARK(sqr(nil))) MARK(add(sqr(x0), x1)) -> c16(MARK(sqr(x0))) MARK(add(add(x0, terms(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(add(x0, terms(z0)))) MARK(add(add(x0, sqr(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(add(x0, sqr(z0)))) MARK(add(add(x0, add(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, add(z0, z1)))) MARK(add(add(x0, dbl(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(add(x0, dbl(z0)))) MARK(add(add(x0, first(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(add(x0, first(z0, z1)))) MARK(add(add(x0, cons(z0, z1)), x2)) -> c16(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(add(x0, cons(z0, z1)))) MARK(add(add(x0, recip(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(add(x0, recip(z0)))) MARK(add(add(x0, s(z0)), x2)) -> c16(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(add(x0, s(z0)))) MARK(add(add(x0, 0), x2)) -> c16(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(add(x0, 0))) MARK(add(add(x0, nil), x2)) -> c16(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(add(x0, nil))) MARK(add(add(terms(z0), x1), x2)) -> c16(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(add(terms(z0), x1))) MARK(add(add(sqr(z0), x1), x2)) -> c16(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(add(sqr(z0), x1))) MARK(add(add(add(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(add(z0, z1), x1))) MARK(add(add(dbl(z0), x1), x2)) -> c16(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(add(dbl(z0), x1))) MARK(add(add(first(z0, z1), x1), x2)) -> c16(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(add(first(z0, z1), x1))) MARK(add(add(cons(z0, z1), x1), x2)) -> c16(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(add(cons(z0, z1), x1))) MARK(add(add(recip(z0), x1), x2)) -> c16(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(add(recip(z0), x1))) MARK(add(add(s(z0), x1), x2)) -> c16(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(add(s(z0), x1))) MARK(add(add(0, x1), x2)) -> c16(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(add(0, x1))) MARK(add(add(nil, x1), x2)) -> c16(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(add(nil, x1))) MARK(add(add(x0, x1), x2)) -> c16(MARK(add(x0, x1))) MARK(add(dbl(terms(z0)), x1)) -> c16(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(dbl(terms(z0)))) MARK(add(dbl(sqr(z0)), x1)) -> c16(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(dbl(sqr(z0)))) MARK(add(dbl(add(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(dbl(add(z0, z1)))) MARK(add(dbl(dbl(z0)), x1)) -> c16(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(dbl(dbl(z0)))) MARK(add(dbl(first(z0, z1)), x1)) -> c16(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(dbl(first(z0, z1)))) MARK(add(dbl(cons(z0, z1)), x1)) -> c16(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(dbl(cons(z0, z1)))) MARK(add(dbl(recip(z0)), x1)) -> c16(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(dbl(recip(z0)))) MARK(add(dbl(s(z0)), x1)) -> c16(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(dbl(s(z0)))) MARK(add(dbl(0), x1)) -> c16(A__ADD(a__dbl(0), mark(x1)), MARK(dbl(0))) MARK(add(dbl(nil), x1)) -> c16(A__ADD(a__dbl(nil), mark(x1)), MARK(dbl(nil))) MARK(add(dbl(x0), x1)) -> 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terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0)) MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0)) MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, dbl(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1)))) MARK(first(x0, first(x1, x2))) -> c19(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), first(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(recip(z0), first(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0))) MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(0, first(x1, x2))) -> c19(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, first(x1, x2))) -> c19(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil)) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (251) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(nil, first(x1, x2))) -> c19(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil)) MARK(first(0, first(x1, x2))) -> c19(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0)) ---------------------------------------- (252) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), 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c17(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(add(x1, first(z0, z1)))) MARK(add(x0, add(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(add(x1, cons(z0, z1)))) MARK(add(x0, add(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(add(x1, recip(z0)))) MARK(add(x0, add(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(add(x1, s(z0)))) MARK(add(x0, add(x1, 0))) -> c17(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(add(x1, 0))) MARK(add(x0, add(x1, nil))) -> c17(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(add(x1, nil))) MARK(add(x0, add(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(add(terms(z0), x2))) MARK(add(x0, add(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(add(sqr(z0), x2))) MARK(add(x0, add(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(add(add(z0, z1), x2))) MARK(add(x0, add(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(add(dbl(z0), x2))) MARK(add(x0, add(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(add(first(z0, z1), x2))) MARK(add(x0, add(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(add(cons(z0, z1), x2))) MARK(add(x0, add(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(add(recip(z0), x2))) MARK(add(x0, add(s(z0), x2))) -> c17(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(add(s(z0), x2))) MARK(add(x0, add(0, x2))) -> c17(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(add(0, x2))) MARK(add(x0, add(nil, x2))) -> c17(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(add(nil, x2))) MARK(add(terms(z0), add(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(add(x1, x2))) MARK(add(sqr(z0), add(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), 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a__dbl(a__sqr(mark(z0)))), MARK(dbl(sqr(z0)))) MARK(add(x0, dbl(add(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(dbl(add(z0, z1)))) MARK(add(x0, dbl(dbl(z0)))) -> c17(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(dbl(dbl(z0)))) MARK(add(x0, dbl(first(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(dbl(first(z0, z1)))) MARK(add(x0, dbl(cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(dbl(cons(z0, z1)))) MARK(add(x0, dbl(recip(z0)))) -> c17(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(dbl(recip(z0)))) MARK(add(x0, dbl(s(z0)))) -> c17(A__ADD(mark(x0), a__dbl(s(z0))), MARK(dbl(s(z0)))) MARK(add(x0, dbl(0))) -> c17(A__ADD(mark(x0), a__dbl(0)), MARK(dbl(0))) MARK(add(x0, dbl(nil))) -> c17(A__ADD(mark(x0), a__dbl(nil)), MARK(dbl(nil))) MARK(add(terms(z0), dbl(x1))) -> c17(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(sqr(z0), dbl(x1))) -> c17(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(add(z0, z1), dbl(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(dbl(z0), dbl(x1))) -> c17(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(first(z0, z1), dbl(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(0, dbl(x1))) -> c17(A__ADD(0, a__dbl(mark(x1))), MARK(dbl(x1))) MARK(add(x0, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(cons(z0, z1), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(recip(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(s(z0), dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(nil, dbl(x1))) -> c17(MARK(dbl(x1))) MARK(add(x0, first(x1, x2))) -> c17(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(x0, first(x1, terms(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(first(x1, terms(z0)))) MARK(add(x0, first(x1, sqr(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(first(x1, sqr(z0)))) MARK(add(x0, first(x1, add(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(first(x1, add(z0, z1)))) MARK(add(x0, first(x1, dbl(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(first(x1, dbl(z0)))) MARK(add(x0, first(x1, first(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(add(x0, first(x1, cons(z0, z1)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(add(x0, first(x1, recip(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(first(x1, recip(z0)))) MARK(add(x0, first(x1, s(z0)))) -> c17(A__ADD(mark(x0), a__first(mark(x1), s(z0))), MARK(first(x1, s(z0)))) MARK(add(x0, first(x1, 0))) -> c17(A__ADD(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(add(x0, first(x1, nil))) -> c17(A__ADD(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(add(x0, first(terms(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(first(terms(z0), x2))) MARK(add(x0, first(sqr(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(first(sqr(z0), x2))) MARK(add(x0, first(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(first(add(z0, z1), x2))) MARK(add(x0, first(dbl(z0), x2))) -> c17(A__ADD(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(first(dbl(z0), x2))) MARK(add(x0, first(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(add(x0, first(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(add(x0, first(recip(z0), x2))) -> c17(A__ADD(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(first(recip(z0), x2))) MARK(add(x0, first(s(z0), x2))) -> c17(A__ADD(mark(x0), a__first(s(z0), mark(x2))), MARK(first(s(z0), x2))) MARK(add(x0, first(0, x2))) -> c17(A__ADD(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(add(x0, first(nil, x2))) -> c17(A__ADD(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(add(terms(z0), first(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(sqr(z0), first(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(add(z0, z1), first(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(dbl(z0), first(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(first(z0, z1), first(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(0, first(x1, x2))) -> c17(A__ADD(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(add(cons(z0, z1), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(recip(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(s(z0), first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(nil, first(x1, x2))) -> c17(MARK(first(x1, x2))) MARK(add(x0, cons(terms(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__terms(mark(z0)), x2)), MARK(cons(terms(z0), x2))) MARK(add(x0, cons(sqr(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__sqr(mark(z0)), x2)), MARK(cons(sqr(z0), x2))) MARK(add(x0, cons(add(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__add(mark(z0), mark(z1)), x2)), MARK(cons(add(z0, z1), x2))) MARK(add(x0, cons(dbl(z0), x2))) -> c17(A__ADD(mark(x0), cons(a__dbl(mark(z0)), x2)), MARK(cons(dbl(z0), x2))) MARK(add(x0, cons(first(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(add(x0, cons(cons(z0, z1), x2))) -> c17(A__ADD(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(add(x0, cons(recip(z0), x2))) -> c17(A__ADD(mark(x0), cons(recip(mark(z0)), x2)), MARK(cons(recip(z0), x2))) MARK(add(x0, cons(s(z0), x2))) -> c17(A__ADD(mark(x0), cons(s(z0), x2)), MARK(cons(s(z0), x2))) MARK(add(x0, cons(0, x2))) -> c17(A__ADD(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(add(x0, cons(nil, x2))) -> c17(A__ADD(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(add(terms(z0), cons(x1, x2))) -> c17(A__ADD(a__terms(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(sqr(z0), cons(x1, x2))) -> c17(A__ADD(a__sqr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(add(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(dbl(z0), cons(x1, x2))) -> c17(A__ADD(a__dbl(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(first(z0, z1), cons(x1, x2))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(0, cons(x1, x2))) -> c17(A__ADD(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(add(x0, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(cons(z0, z1), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(recip(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(s(z0), cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(nil, cons(x1, x2))) -> c17(MARK(cons(x1, x2))) MARK(add(x0, recip(terms(z0)))) -> c17(A__ADD(mark(x0), recip(a__terms(mark(z0)))), MARK(recip(terms(z0)))) MARK(add(x0, recip(sqr(z0)))) -> c17(A__ADD(mark(x0), recip(a__sqr(mark(z0)))), MARK(recip(sqr(z0)))) MARK(add(x0, recip(add(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__add(mark(z0), mark(z1)))), MARK(recip(add(z0, z1)))) MARK(add(x0, recip(dbl(z0)))) -> c17(A__ADD(mark(x0), recip(a__dbl(mark(z0)))), MARK(recip(dbl(z0)))) MARK(add(x0, recip(first(z0, z1)))) -> c17(A__ADD(mark(x0), recip(a__first(mark(z0), mark(z1)))), MARK(recip(first(z0, z1)))) MARK(add(x0, recip(cons(z0, z1)))) -> c17(A__ADD(mark(x0), recip(cons(mark(z0), z1))), MARK(recip(cons(z0, z1)))) MARK(add(x0, recip(recip(z0)))) -> c17(A__ADD(mark(x0), recip(recip(mark(z0)))), MARK(recip(recip(z0)))) MARK(add(x0, recip(s(z0)))) -> c17(A__ADD(mark(x0), recip(s(z0))), MARK(recip(s(z0)))) MARK(add(x0, recip(0))) -> c17(A__ADD(mark(x0), recip(0)), MARK(recip(0))) MARK(add(x0, recip(nil))) -> c17(A__ADD(mark(x0), recip(nil)), MARK(recip(nil))) MARK(add(terms(z0), recip(x1))) -> c17(A__ADD(a__terms(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(sqr(z0), recip(x1))) -> c17(A__ADD(a__sqr(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(add(z0, z1), recip(x1))) -> c17(A__ADD(a__add(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(dbl(z0), recip(x1))) -> c17(A__ADD(a__dbl(mark(z0)), recip(mark(x1))), MARK(recip(x1))) MARK(add(first(z0, z1), recip(x1))) -> c17(A__ADD(a__first(mark(z0), mark(z1)), recip(mark(x1))), MARK(recip(x1))) MARK(add(0, recip(x1))) -> c17(A__ADD(0, recip(mark(x1))), MARK(recip(x1))) MARK(add(x0, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(cons(z0, z1), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(recip(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(s(z0), recip(x1))) -> c17(MARK(recip(x1))) MARK(add(nil, recip(x1))) -> c17(MARK(recip(x1))) MARK(add(terms(terms(z0)), x1)) -> c17(A__ADD(a__terms(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(sqr(z0)), x1)) -> c17(A__ADD(a__terms(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(add(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(dbl(z0)), x1)) -> c17(A__ADD(a__terms(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(first(z0, z1)), x1)) -> c17(A__ADD(a__terms(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(terms(cons(z0, z1)), x1)) -> c17(A__ADD(a__terms(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(terms(recip(z0)), x1)) -> c17(A__ADD(a__terms(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(terms(s(z0)), x1)) -> c17(A__ADD(a__terms(s(z0)), mark(x1)), MARK(x1)) MARK(add(terms(0), x1)) -> c17(A__ADD(a__terms(0), mark(x1)), MARK(x1)) MARK(add(terms(nil), x1)) -> c17(A__ADD(a__terms(nil), mark(x1)), MARK(x1)) MARK(add(terms(x0), s(z0))) -> c17(A__ADD(a__terms(mark(x0)), s(z0))) MARK(add(terms(x0), 0)) -> c17(A__ADD(a__terms(mark(x0)), 0)) MARK(add(terms(x0), nil)) -> c17(A__ADD(a__terms(mark(x0)), nil)) MARK(add(terms(x0), x1)) -> c17(MARK(x1)) MARK(add(sqr(terms(z0)), x1)) -> c17(A__ADD(a__sqr(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(sqr(z0)), x1)) -> c17(A__ADD(a__sqr(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(add(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(dbl(z0)), x1)) -> c17(A__ADD(a__sqr(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(first(z0, z1)), x1)) -> c17(A__ADD(a__sqr(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(sqr(cons(z0, z1)), x1)) -> c17(A__ADD(a__sqr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(sqr(recip(z0)), x1)) -> c17(A__ADD(a__sqr(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(sqr(s(z0)), x1)) -> c17(A__ADD(a__sqr(s(z0)), mark(x1)), MARK(x1)) MARK(add(sqr(0), x1)) -> c17(A__ADD(a__sqr(0), mark(x1)), MARK(x1)) MARK(add(sqr(nil), x1)) -> c17(A__ADD(a__sqr(nil), mark(x1)), MARK(x1)) MARK(add(sqr(x0), s(z0))) -> c17(A__ADD(a__sqr(mark(x0)), s(z0))) MARK(add(sqr(x0), 0)) -> c17(A__ADD(a__sqr(mark(x0)), 0)) MARK(add(sqr(x0), nil)) -> c17(A__ADD(a__sqr(mark(x0)), nil)) MARK(add(sqr(x0), x1)) -> c17(MARK(x1)) MARK(add(add(x0, terms(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, sqr(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, dbl(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(add(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__add(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(add(x0, recip(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(add(x0, s(z0)), x2)) -> c17(A__ADD(a__add(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(add(x0, 0), x2)) -> c17(A__ADD(a__add(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(add(x0, nil), x2)) -> c17(A__ADD(a__add(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(add(terms(z0), x1), x2)) -> c17(A__ADD(a__add(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(sqr(z0), x1), x2)) -> c17(A__ADD(a__add(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(add(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(dbl(z0), x1), x2)) -> c17(A__ADD(a__add(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(first(z0, z1), x1), x2)) -> c17(A__ADD(a__add(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__add(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(recip(z0), x1), x2)) -> c17(A__ADD(a__add(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(s(z0), x1), x2)) -> c17(A__ADD(a__add(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(0, x1), x2)) -> c17(A__ADD(a__add(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(nil, x1), x2)) -> c17(A__ADD(a__add(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(add(x0, x1), s(z0))) -> c17(A__ADD(a__add(mark(x0), mark(x1)), s(z0))) MARK(add(add(x0, x1), 0)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), 0)) MARK(add(add(x0, x1), nil)) -> c17(A__ADD(a__add(mark(x0), mark(x1)), nil)) MARK(add(add(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(dbl(terms(z0)), x1)) -> c17(A__ADD(a__dbl(a__terms(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(sqr(z0)), x1)) -> c17(A__ADD(a__dbl(a__sqr(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(add(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__add(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(dbl(z0)), x1)) -> c17(A__ADD(a__dbl(a__dbl(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(first(z0, z1)), x1)) -> c17(A__ADD(a__dbl(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(add(dbl(cons(z0, z1)), x1)) -> c17(A__ADD(a__dbl(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(add(dbl(recip(z0)), x1)) -> c17(A__ADD(a__dbl(recip(mark(z0))), mark(x1)), MARK(x1)) MARK(add(dbl(s(z0)), x1)) -> c17(A__ADD(a__dbl(s(z0)), mark(x1)), MARK(x1)) MARK(add(dbl(0), x1)) -> c17(A__ADD(a__dbl(0), mark(x1)), MARK(x1)) MARK(add(dbl(nil), x1)) -> c17(A__ADD(a__dbl(nil), mark(x1)), MARK(x1)) MARK(add(dbl(x0), s(z0))) -> c17(A__ADD(a__dbl(mark(x0)), s(z0))) MARK(add(dbl(x0), 0)) -> c17(A__ADD(a__dbl(mark(x0)), 0)) MARK(add(dbl(x0), nil)) -> c17(A__ADD(a__dbl(mark(x0)), nil)) MARK(add(dbl(x0), x1)) -> c17(MARK(x1)) MARK(add(first(x0, terms(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0)) MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0)) MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, dbl(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1)))) MARK(first(x0, first(x1, x2))) -> c19(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), first(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(recip(z0), first(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0))) MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 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c17(A__ADD(a__first(mark(x0), a__terms(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, sqr(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__sqr(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, add(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__add(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, dbl(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), a__dbl(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, first(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(add(first(x0, cons(z0, z1)), x2)) -> c17(A__ADD(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(add(first(x0, recip(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), recip(mark(z0))), mark(x2)), MARK(x2)) MARK(add(first(x0, s(z0)), x2)) -> c17(A__ADD(a__first(mark(x0), s(z0)), mark(x2)), MARK(x2)) MARK(add(first(x0, 0), x2)) -> c17(A__ADD(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(add(first(x0, nil), x2)) -> c17(A__ADD(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(add(first(terms(z0), x1), x2)) -> c17(A__ADD(a__first(a__terms(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(sqr(z0), x1), x2)) -> c17(A__ADD(a__first(a__sqr(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(add(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__add(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(dbl(z0), x1), x2)) -> c17(A__ADD(a__first(a__dbl(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(first(z0, z1), x1), x2)) -> c17(A__ADD(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(cons(z0, z1), x1), x2)) -> c17(A__ADD(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(recip(z0), x1), x2)) -> c17(A__ADD(a__first(recip(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(s(z0), x1), x2)) -> c17(A__ADD(a__first(s(z0), mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(0, x1), x2)) -> c17(A__ADD(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(nil, x1), x2)) -> c17(A__ADD(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(add(first(x0, x1), s(z0))) -> c17(A__ADD(a__first(mark(x0), mark(x1)), s(z0))) MARK(add(first(x0, x1), 0)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), 0)) MARK(add(first(x0, x1), nil)) -> c17(A__ADD(a__first(mark(x0), mark(x1)), nil)) MARK(add(first(x0, x1), x2)) -> c17(MARK(x2)) MARK(add(0, s(x1))) -> c17(A__ADD(0, s(x1))) MARK(add(0, 0)) -> c17(A__ADD(0, 0)) MARK(add(0, nil)) -> c17(A__ADD(0, nil)) MARK(first(x0, terms(x1))) -> c19(A__FIRST(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(first(x0, terms(terms(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, terms(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, terms(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, terms(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, terms(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, terms(recip(z0)))) -> c19(A__FIRST(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(first(x0, terms(s(z0)))) -> c19(A__FIRST(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(first(x0, terms(0))) -> c19(A__FIRST(mark(x0), a__terms(0)), MARK(x0)) MARK(first(x0, terms(nil))) -> c19(A__FIRST(mark(x0), a__terms(nil)), MARK(x0)) MARK(first(terms(z0), terms(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), terms(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), terms(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), terms(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), terms(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, terms(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), terms(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), terms(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), terms(x1))) -> c19(A__FIRST(s(z0), a__terms(mark(x1)))) MARK(first(x0, sqr(terms(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0)) MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0)) MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, dbl(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1)))) MARK(first(x0, first(x1, x2))) -> c19(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(cons(z0, z1), first(x1, x2))) -> c19(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(recip(z0), first(x1, x2))) -> c19(A__FIRST(recip(mark(z0)), a__first(mark(x1), mark(x2))), MARK(recip(z0))) MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2 ---------------------------------------- (253) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (254) Obligation: Complexity Dependency Tuples Problem Rules: a__terms(z0) -> cons(recip(a__sqr(mark(z0))), terms(s(z0))) a__terms(z0) -> terms(z0) a__sqr(0) -> 0 a__sqr(s(z0)) -> s(add(sqr(z0), dbl(z0))) a__sqr(z0) -> sqr(z0) a__dbl(0) -> 0 a__dbl(s(z0)) -> s(s(dbl(z0))) a__dbl(z0) -> dbl(z0) a__add(0, z0) -> mark(z0) a__add(s(z0), z1) -> s(add(z0, z1)) a__add(z0, z1) -> add(z0, z1) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) mark(terms(z0)) -> a__terms(mark(z0)) mark(sqr(z0)) -> a__sqr(mark(z0)) mark(add(z0, z1)) -> a__add(mark(z0), mark(z1)) mark(dbl(z0)) -> a__dbl(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(recip(z0)) -> recip(mark(z0)) mark(s(z0)) -> s(z0) mark(0) -> 0 mark(nil) -> nil Tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), a__terms(recip(mark(z0)))), MARK(x0)) MARK(add(x0, terms(s(z0)))) -> c16(A__ADD(mark(x0), a__terms(s(z0))), MARK(x0)) MARK(add(x0, terms(0))) -> c16(A__ADD(mark(x0), a__terms(0)), MARK(x0)) MARK(add(x0, terms(nil))) -> c16(A__ADD(mark(x0), a__terms(nil)), MARK(x0)) MARK(add(terms(z0), terms(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__terms(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), terms(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__terms(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), terms(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), terms(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__terms(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), terms(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__terms(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), terms(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), terms(x1))) -> c16(MARK(recip(z0))) MARK(add(0, terms(x1))) -> c16(A__ADD(0, a__terms(mark(x1)))) MARK(add(x0, sqr(x1))) -> c16(A__ADD(mark(x0), sqr(mark(x1))), MARK(x0)) MARK(add(x0, sqr(terms(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(sqr(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(dbl(z0)))) -> c16(A__ADD(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, sqr(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, sqr(recip(z0)))) -> c16(A__ADD(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(add(x0, sqr(s(z0)))) -> c16(A__ADD(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(add(x0, sqr(0))) -> c16(A__ADD(mark(x0), a__sqr(0)), MARK(x0)) MARK(add(x0, sqr(nil))) -> c16(A__ADD(mark(x0), a__sqr(nil)), MARK(x0)) MARK(add(terms(z0), sqr(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), sqr(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), sqr(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), sqr(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), sqr(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), sqr(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), sqr(x1))) -> c16(MARK(recip(z0))) MARK(add(0, sqr(x1))) -> c16(A__ADD(0, a__sqr(mark(x1)))) MARK(add(x0, add(x1, x2))) -> c16(A__ADD(mark(x0), add(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, add(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, add(x1, cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, add(x1, recip(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(add(x0, add(x1, s(z0)))) -> c16(A__ADD(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(add(x0, add(x1, 0))) -> c16(A__ADD(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(add(x0, add(x1, nil))) -> c16(A__ADD(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(add(x0, add(terms(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(sqr(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(add(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(dbl(z0), x2))) -> c16(A__ADD(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(first(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(add(x0, add(cons(z0, z1), x2))) -> c16(A__ADD(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(add(x0, add(recip(z0), x2))) -> c16(A__ADD(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(add(x0, add(s(z0), x2))) -> c16(A__ADD(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(add(x0, add(0, x2))) -> c16(A__ADD(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(add(x0, add(nil, x2))) -> c16(A__ADD(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(add(terms(z0), add(x1, x2))) -> c16(A__ADD(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(add(sqr(z0), add(x1, x2))) -> c16(A__ADD(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(add(add(z0, z1), add(x1, x2))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(add(dbl(z0), add(x1, x2))) -> c16(A__ADD(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(add(first(z0, z1), add(x1, x2))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), add(x1, x2))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), add(x1, x2))) -> c16(MARK(recip(z0))) MARK(add(0, add(x1, x2))) -> c16(A__ADD(0, a__add(mark(x1), mark(x2)))) MARK(add(x0, dbl(x1))) -> c16(A__ADD(mark(x0), dbl(mark(x1))), MARK(x0)) MARK(add(x0, dbl(terms(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(sqr(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(dbl(z0)))) -> c16(A__ADD(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, dbl(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, dbl(recip(z0)))) -> c16(A__ADD(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(add(x0, dbl(s(z0)))) -> c16(A__ADD(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(add(x0, dbl(0))) -> c16(A__ADD(mark(x0), a__dbl(0)), MARK(x0)) MARK(add(x0, dbl(nil))) -> c16(A__ADD(mark(x0), a__dbl(nil)), MARK(x0)) MARK(add(terms(z0), dbl(x1))) -> c16(A__ADD(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(add(sqr(z0), dbl(x1))) -> c16(A__ADD(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(add(add(z0, z1), dbl(x1))) -> c16(A__ADD(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(add(dbl(z0), dbl(x1))) -> c16(A__ADD(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(add(first(z0, z1), dbl(x1))) -> c16(A__ADD(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(add(cons(z0, z1), dbl(x1))) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), dbl(x1))) -> c16(MARK(recip(z0))) MARK(add(0, dbl(x1))) -> c16(A__ADD(0, a__dbl(mark(x1)))) MARK(add(x0, first(x1, x2))) -> c16(A__ADD(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(add(x0, first(x1, terms(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, sqr(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, add(z0, z1)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, first(x1, dbl(z0)))) -> c16(A__ADD(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, first(x1, first(z0, z1)))) -> c16(A__ADD(mark(x0), 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c19(A__FIRST(mark(x0), a__sqr(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sqr(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__sqr(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sqr(recip(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(recip(mark(z0)))), MARK(x0)) MARK(first(x0, sqr(s(z0)))) -> c19(A__FIRST(mark(x0), a__sqr(s(z0))), MARK(x0)) MARK(first(x0, sqr(0))) -> c19(A__FIRST(mark(x0), a__sqr(0)), MARK(x0)) MARK(first(x0, sqr(nil))) -> c19(A__FIRST(mark(x0), a__sqr(nil)), MARK(x0)) MARK(first(terms(z0), sqr(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__sqr(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), sqr(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__sqr(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), sqr(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), sqr(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__sqr(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), sqr(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__sqr(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, sqr(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), sqr(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), sqr(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), sqr(x1))) -> c19(A__FIRST(s(z0), a__sqr(mark(x1)))) MARK(first(x0, add(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, add(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, add(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, add(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, add(x1, 0))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), 0)), MARK(x0)) MARK(first(x0, add(x1, nil))) -> c19(A__FIRST(mark(x0), a__add(mark(x1), nil)), MARK(x0)) MARK(first(x0, add(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, add(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__add(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, add(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, add(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__add(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, add(0, x2))) -> c19(A__FIRST(mark(x0), a__add(0, mark(x2))), MARK(x0)) MARK(first(x0, add(nil, x2))) -> c19(A__FIRST(mark(x0), a__add(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), add(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__add(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), add(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__add(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), add(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__add(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), add(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__add(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, add(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), add(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), add(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), add(x1, x2))) -> c19(A__FIRST(s(z0), a__add(mark(x1), mark(x2)))) MARK(first(x0, dbl(terms(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(sqr(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(dbl(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, dbl(cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__dbl(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, dbl(recip(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(recip(mark(z0)))), MARK(x0)) MARK(first(x0, dbl(s(z0)))) -> c19(A__FIRST(mark(x0), a__dbl(s(z0))), MARK(x0)) MARK(first(x0, dbl(0))) -> c19(A__FIRST(mark(x0), a__dbl(0)), MARK(x0)) MARK(first(x0, dbl(nil))) -> c19(A__FIRST(mark(x0), a__dbl(nil)), MARK(x0)) MARK(first(terms(z0), dbl(x1))) -> c19(A__FIRST(a__terms(mark(z0)), a__dbl(mark(x1))), MARK(terms(z0))) MARK(first(sqr(z0), dbl(x1))) -> c19(A__FIRST(a__sqr(mark(z0)), a__dbl(mark(x1))), MARK(sqr(z0))) MARK(first(add(z0, z1), dbl(x1))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(add(z0, z1))) MARK(first(dbl(z0), dbl(x1))) -> c19(A__FIRST(a__dbl(mark(z0)), a__dbl(mark(x1))), MARK(dbl(z0))) MARK(first(first(z0, z1), dbl(x1))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__dbl(mark(x1))), MARK(first(z0, z1))) MARK(first(x0, dbl(x1))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), dbl(x1))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), dbl(x1))) -> c19(MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1)))) MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, first(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), first(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2)))) S tuples: A__ADD(0, z0) -> c8(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c12(MARK(z1)) MARK(terms(z0)) -> c14(A__TERMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c21(MARK(z0)) MARK(recip(z0)) -> c22(MARK(z0)) A__TERMS(z0) -> c(MARK(z0)) MARK(sqr(z0)) -> c15(MARK(z0)) MARK(dbl(z0)) -> c18(MARK(z0)) MARK(add(cons(z0, z1), x1)) -> c16(MARK(cons(z0, z1))) MARK(add(recip(z0), x1)) -> c16(MARK(recip(z0))) MARK(add(0, x1)) -> c16(A__ADD(0, mark(x1))) MARK(add(0, x1)) -> c17(A__ADD(0, mark(x1)), MARK(x1)) MARK(add(cons(z0, z1), x1)) -> c17(MARK(x1)) MARK(add(recip(z0), x1)) -> c17(MARK(x1)) MARK(add(s(z0), x1)) -> c17(MARK(x1)) MARK(add(nil, x1)) -> c17(MARK(x1)) MARK(first(x0, cons(z0, z1))) -> c19(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(terms(z0), x1)) -> c19(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(terms(z0))) MARK(first(sqr(z0), x1)) -> c19(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(sqr(z0))) MARK(first(add(z0, z1), x1)) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(add(z0, z1))) MARK(first(dbl(z0), x1)) -> c19(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(dbl(z0))) MARK(first(first(z0, z1), x1)) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(x0, recip(z0))) -> c19(MARK(x0)) MARK(first(x0, s(z0))) -> c19(MARK(x0)) MARK(first(x0, 0)) -> c19(MARK(x0)) MARK(first(x0, nil)) -> c19(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), x1)) -> c19(MARK(recip(z0))) MARK(first(s(z0), x1)) -> c19(A__FIRST(s(z0), mark(x1))) MARK(first(x0, terms(z0))) -> c20(A__FIRST(mark(x0), a__terms(mark(z0))), MARK(terms(z0))) MARK(first(x0, sqr(z0))) -> c20(A__FIRST(mark(x0), a__sqr(mark(z0))), MARK(sqr(z0))) MARK(first(x0, add(z0, z1))) -> c20(A__FIRST(mark(x0), a__add(mark(z0), mark(z1))), MARK(add(z0, z1))) MARK(first(x0, dbl(z0))) -> c20(A__FIRST(mark(x0), a__dbl(mark(z0))), MARK(dbl(z0))) MARK(first(x0, first(z0, z1))) -> c20(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c20(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(terms(z0), x1)) -> c20(A__FIRST(a__terms(mark(z0)), mark(x1)), MARK(x1)) MARK(first(sqr(z0), x1)) -> c20(A__FIRST(a__sqr(mark(z0)), mark(x1)), MARK(x1)) MARK(first(add(z0, z1), x1)) -> c20(A__FIRST(a__add(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(dbl(z0), x1)) -> c20(A__FIRST(a__dbl(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c20(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c20(A__FIRST(s(z0), mark(x1)), MARK(x1)) MARK(first(x0, recip(z0))) -> c20(MARK(recip(z0))) MARK(first(cons(z0, z1), x1)) -> c20(MARK(x1)) MARK(first(recip(z0), x1)) -> c20(MARK(x1)) MARK(first(0, x1)) -> c20(MARK(x1)) MARK(first(nil, x1)) -> c20(MARK(x1)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), cons(recip(a__sqr(mark(mark(x1)))), terms(s(mark(x1))))), MARK(x0)) MARK(add(x0, terms(x1))) -> c16(A__ADD(mark(x0), terms(mark(x1))), MARK(x0)) MARK(add(x0, terms(terms(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__terms(mark(z0)))), MARK(x0)) MARK(add(x0, terms(sqr(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__sqr(mark(z0)))), MARK(x0)) MARK(add(x0, terms(add(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(dbl(z0)))) -> c16(A__ADD(mark(x0), a__terms(a__dbl(mark(z0)))), MARK(x0)) MARK(add(x0, terms(first(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(add(x0, terms(cons(z0, z1)))) -> c16(A__ADD(mark(x0), a__terms(cons(mark(z0), z1))), MARK(x0)) MARK(add(x0, terms(recip(z0)))) -> c16(A__ADD(mark(x0), 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c19(MARK(recip(z0))) MARK(first(s(z0), dbl(x1))) -> c19(A__FIRST(s(z0), a__dbl(mark(x1)))) MARK(first(x0, first(x1, terms(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__terms(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, sqr(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__sqr(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, add(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__add(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, dbl(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__dbl(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, recip(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), recip(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), s(z0))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c19(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(terms(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__terms(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(sqr(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__sqr(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(add(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__add(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(dbl(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(a__dbl(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c19(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(recip(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(recip(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c19(A__FIRST(mark(x0), a__first(s(z0), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c19(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c19(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(terms(z0), first(x1, x2))) -> c19(A__FIRST(a__terms(mark(z0)), a__first(mark(x1), mark(x2))), MARK(terms(z0))) MARK(first(sqr(z0), first(x1, x2))) -> c19(A__FIRST(a__sqr(mark(z0)), a__first(mark(x1), mark(x2))), MARK(sqr(z0))) MARK(first(add(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__add(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(add(z0, z1))) MARK(first(dbl(z0), first(x1, x2))) -> c19(A__FIRST(a__dbl(mark(z0)), a__first(mark(x1), mark(x2))), MARK(dbl(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c19(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(x0, first(x1, x2))) -> c19(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c19(MARK(cons(z0, z1))) MARK(first(recip(z0), first(x1, x2))) -> c19(MARK(recip(z0))) MARK(first(s(z0), first(x1, x2))) -> c19(A__FIRST(s(z0), a__first(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__terms_1, a__sqr_1, a__dbl_1, a__add_2, a__first_2, mark_1 Defined Pair Symbols: A__ADD_2, A__FIRST_2, MARK_1, A__TERMS_1 Compound Symbols: c8_1, c12_1, c14_2, c21_1, c22_1, c_1, c15_1, c18_1, c16_1, c17_2, c17_1, c19_2, c19_1, c20_2, c20_1, c16_2